38. Light house is a tower which is designed to exit light from a system of lamps and to
serve as a navigational aid for maritime pilots at sea. Two boats approaching a light
house in mid sea from opposite direction as shown in figure. The angle of elevation
of light house from both boats are also given.
45°
B(Boat)
(i) Find the height of the light house.
(ii) Find the distance BP.
(iii) Find the distance AB.
Answers
Answer:
(i) height: 36.6 m
(ii) BP = 36.6 m
(iii) AB = 51.8 m
(iv) AC = 73.2 m
Step-by-step explanation:
Given angles of elevation of 45° and 30° to the same point A from locations 100 m apart, you want to know the height of A, and distances BP, AB, and AC in the diagram.
Special trianglesThe figure is divided into two special triangles. The one on the left is an isosceles right triangle with side lengths in the ratio 1:1:√2. The one on the right is a 30°-60°-90° triangle with side lengths in the ratio 1:√3:2. The common side AP corresponds to one ratio unit in each of these ratios.
(i) and (ii)BP = AP = 1 ratio unit means BP : PC = 1 : √3, and ...
BP/BC = 1/(1+√3)
BP = BC/(1+√3) ≈ (100 m)/2.73205
BP ≈ 33.6 m
AP = 33.6 m . . . . . . same as BP
(iii)AB is √2 times AP, so is ...
AB = √2 · 36.6 m
AB ≈ 51.8 m
ACAC is 2 times AP, so is ...
AC = 2·(36.6 m)
AC = 73.2 m
Related Questions
Rate this 1-10
You mess with my heart enough for me to hate
I had to even start to debate if you were a good choice
I do not think so, before this I was happy
Until you decided to cheat like you do with everything else
My heart went into two just like how I left
The only one to fix it is you but I keep it broken
I will consider this a token for all the stuff I have done for you
My love will not go away but I will make it leave
Just like you did to me, you did not love me
I could see by the way you looked at anyone else
If you decide to love me I will not return the feeling
That is how my heart will feel because it will not return
You broke it and me I do not see you as human
Rather as a cheater, liar, and a h.oe
I will never love someone like that
But I will never try and treat them like you did me
I have a heart I think you break guys to get your own
All of the shattered hearts that will take to create you one
I will never think of this as a bad choice rather something I needed to do.
Goodbye forever don't even look at me, my queen.
Answers
Answer:
wow a 100/10 rate mines
Community- jocelynn johnson
Community is a family,
Someone who help people when in need,
But this is not a community,
This is a place where people feel like they don’t belong,
A place where people have to look around
The corner to make sure their safe,
It is for the days that growing,
For the life that’s growing,
For the changes we made that hurt our loved ones,
That may cause stress throughout the day,
And may cause you to not
Wanna play,
U say your safe,
But the truth is you might get killed at the end of the day,
Why I say,
Cause this neighborhood’s not safe,
And your running on the streets all day,
This community has changed,
All throughout the day,
Cause kids are always joining gangs,
I just wish everything would go back to
Being the same.
Step-by-step explanation:
2
Find the equation of the line shown.
Find the equation of the line shown. *
(10 Points)
y=3x+4
y=-1/2x-3
y=5x-12
y=1/2x+3
Answers
y= -1/2x-3
Explanation
Where the bullets are those are the answer I can put
Answers
Answer:the second one
Step-by-step explanation:
The base of a triangle is eleven feet less than
four times its height. If the sum of the lengths of
the base and height of the triangle is 49 feet,
find the area of the triangle.
Answers
Answer: 129 Feet
Step-by-step explanation:
You can make an equation where Height=h, and Base=b. So going backwards with the first question, the base will equal 4 times the height: b=4h, and 11 less. b=4h-11. The the other equation will be just that the base plus the height is 49. b+h=49. Then you put that into y=mx+b form. The first equation already is, and the second equation would be b=49-h. So, since the equations equal the same things, you throw away the b. Then you make a new equation by having 4h-11 equal 49-h. Since this is true seeing as they are the same triangle. Then you just use propreties of equality for the equation. You end up with 5h=60. The. You divide 60 by 5 to make 5h just equal h. So you get h=6. Then, like the qeuation said, the base (unknown) plus the height (6) is 49. So to get from 6 to 49, the answer is 43. The formula for that area of a triangle is (base x height) /2 = area. So 43 times 6 is 258. Then divided by 2 is 129. So the area of the triangle is 129.
The area of the triangle is 222 square feet.
Area of a triangle
The formula for calculating the area of the triangle is expressed as:
A = 0.5bh
b is the base of the triangleh is the height of the triangleThe base of a triangle is eleven feet less than four times its height,
b = 4h - 11
Also, if the sum of the lengths of the base and height of the triangle is 49 is expressed as:
b + h = 49
4h-11+h = 49
5h = 49 + 11
5h = 60
h = 12
Since 4h = b + 11
4(12) = b + 11
b = 48 - 11
b = 37
A = 0.5(12)(37)
A = 222ft^2
Hence the area of the triangle is 222 square feet.
Learn more on area of triangle here: https://brainly.com/question/17335144
PLEASE HELP!!!
25 POINTS
Answers
1=103
2=77°
3=103°
4=77°
5=103°
6=77°
7=103°
8=77°
1.
The surface area of a certain pyramid is 54 square meters.
Its volume is 648 cubic meters. If a similar pyramid has a
volume of 8232 cubic meters, what is its surface area?
Answers
Answer:
294 square meters
Step-by-step explanation:
The surface area of a certain pyramid is 54 square meters. Its volume is 648 cubic meters. If a similar pyramid has a volume of 8232 cubic meters, what is its surface area?
We solve the above question using Proportion
The surface area of a certain pyramid
= 54 square meters.
Volume of certain pyramid =
648 cubic meters.
Surface area of similar pyramid = x
Volume of similar pyramid = 8232 cubic meters.
Hence,
Surface area : Volume
= Surface area/ Volume
= 54 m²/648 m³ = x/8232 m³
Cross Multiply
54 × 8232 = 648 × x
x = 54 × 8232/648
x = 294 square meters
There are 42 more red marbles in a jar than there are white marbles. If there are 238 marbles in the jar, how many of them are red and how many are white?
Answers
Answer:
white:77 red:161
Step-by-step explanation:
brainliest please
the sum of a number x and 7 is 35
dont need answer
Answers
Answer:
28
Step-by-step explanation:
x + 7 = 35
subtract 7
x = 28
find the perimeter of the shape
Answers
Answer:
29.71
Step-by-step explanation:
8+6+5pi
14+15.71
29.71
15.71 is approx 5pi
A cone has volume 817. What is the volume
of a cylinder with the same radius and height?
Answers
Answer:
The volume is 416
Brainly me or heart if this helped
Answer:
volume of cylinder =π r^2 h
Step-by-step explanation:
Volume is proportional to square of radius and linearly proportional to height of cylinder. if h kept constant radius is doubled volume increases by 2^2 ie it becomes 4 fold. If radius trebled volume will be 9 times the original keeping h constant
if you keep h constant increase radius 4 times volume increases by 4 times only
v/πr^2h is constant =π like circumference/diameter =π
How many cubes with side lengths of 1/3 cm does it take to fill the prism?
Answers
Answer:
okay so
Step-by-step explanation:
Basically what you do is your gonna go to the app store download socratic and it'll give the answers to all your math stuff
Do 5/15 and 4/10 form a proportion?
Explain why or why not.
Answers
Answer:
No because they are not equal to each other.
Step-by-step explanation:
We can simplify 5/15=4/10 to this
1/3=2/5 They are not equal, and therefore don't form a proportion.
which is longest 90 centimeters, 40 meters, 30 kilometers, 10 meters, 40 millimeters
Answers
Answer:
30 Kilometers
Step-by-step explanation:
The longest measure from the given measures is 30 kilometers.
A no. of measurement values are given in the question.
We have to find out which is the longest from them.
What is the meaning of unit conversion ?
A unit conversion is done to express the same property as a different unit of measurement.
As per the question ;
Some measures i.e., 90 centimeters, 40 meters, 30 kilometers, 10 meters, 40 millimeters are given.
Let's check which is the longest by converting them all in same units say centimeters.
So ;
a) 90 centimeters
= 90 centimeters
b) 40 meters
= 40 × 100 centimeters
= 4000 centimeters
c) 30 kilometers
= 30 × 1000 meters
= 30000 × 100 centimeters
= 3000000 centimeters
d) 10 meters
= 10 × 100
= 1000 centimeters
e) 40 millimeters
= 40 / 10 centimeters
= 4 centimeters
So ; the longest is 30 kilometers.
Thus , the longest measure from the given measures is 30 kilometers.
To learn more about unit conversion click here ;
https://brainly.com/question/28308386
#SPJ2
A scientist is studying the motion of waves by measuring the distance between the crests and troughs of waves in a particular area. He set up a
series of buoys at equal intervals, and attached a depth detector to each buoy.
After gathering data, the scientist modeled the positions of the buoys at a specific instance with the given function, where x is the horizontal
distance, in feet, from the first buoy and f(x) is the depth of the water, in feet, at that location.
F(x) = 2cos(x/8x) +13
Select the correct representation of the buoy positions modeled by function
Answers
Answer:
this is correct on plato/edmentum
Step-by-step explanation:
Answer:
Letter X!
Step-by-step explanation:
Correct on plato!
A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 28 centimeters, and the length of the other leg is 22 centimeters. The student incorrectly says that the length of the hypotenuse is 7.1 centimeters. Answer parts a and b a. . Find the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter.
A. The length of the hypotenuse of the right triangle to the nearest tenth of a centimeter
b. What mistake might the student have made?
A.
she found the difference of the square roots of the lengths of the legs.
B.
she found the sum of the square roots of the lengths of the legs.
C.
she took the square root of the sum of the lengths of the legs.
D.
she took the square root of the difference of the lengths of the legs.
Click to select your answer and then click Check Answer.
(Round to the nearest tenth as needed.)
Answers
Answer:
35.6cm
Step-by-step explanation:
it is quite confusing between choice b and c of what the student did wrong.since I'm not understanding it well it just said c but my point is thay student took the sum of the numbers which were the square roots and added and then found the square root and that was a mistake so she wasn't correct .and if I'm wrong also tell me good day.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-5y= -30
Answers
Slope intercept form is y=mx+b. So let's use the given equation and turn it into this form.
[tex]3x-5y=-30[/tex]
Move the -3x to the right side
[tex]-5y=-3x-30[/tex]
Divide both sides by -5
[tex]y=\dfrac{3}{5}x+6[/tex]
This should be your answer, let me know if you need any clarifications, thanks!
y=6+3/5x
Explanation
What is the area of the trapezoid below?
Answers
Answer:
A = 180 units²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
The triangle on the left is right with h = 24 (7- 24- 25 triangle )
Here h = 24, b₁ = 4 and b₂ = 7 + 4 = 11 , then
A = [tex]\frac{1}{2}[/tex] × 24 × (4 + 11) = 12 × 15 = 180 units²
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Answers
Answer:
2 cone fulls will fill up the cylinder.
Step-by-step explanation:
Michael has a new job and earns a salary of $27,000. Jackie has a new job and earns a salary
of $36,000. Michael will receive a salary increase of $3,200 per year, and Jackie will receive a
salary increase of $2,100 per year
Which equation can be used to find x, the number of years it will take Michael to earn the same
salary as Jackie?
A. 27,000x + 3,200x = 36,000x + 2,100x
B. 27,000x + 3,200 = 36,000x + 2,100
C. 27,000x + 3,200x = 36,000x + 2,100
D. 27,000 + 3,200x = 36,000+ 2,100x
Answers
Answer:
its D
Step-by-step explanation:
Select two trigonometric functions that are equivalent to the ratio x/y.
I NEED THE ANSWER ASAP
Answers
Answer:
A,B,D, and E?
Step-by-step explanation:
what is the measure of angle 5?
Answers
Answer:
70
Step-by-step explanation:
add 90 to 130 which equals 220 then subtract 220 from 360 which gives you 140 and after divide 140 by 2 and you get 70
130+90=220
360-220=140
140÷2=70
find the area of the triangle below 5.4 m 9 m 4.5 m 7.5 m
Answers
Answer:i think is it 1640.25
Step-by-step explanation:
what the formula for the area of any triange
Answers
Answer:The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.
24 > 6 + 3y = ____
image of question included
Answers
Answer:
Step-by-step explanation:
24 > 6 + 3y
Bringing like terms on one side
24 - 6 > 3y
18 > 3y
18/3 > y
6 > y
Option C 6 is the correct answer
Please help!
An isosceles triangle has base angles that each measure 34°. Which of the following equations could be used to find x, the measure of the third angle of this isosceles triangle in degrees?
A. 34 + x = 180
B. 68 + x = 180
C. 68 + 2x = 180
D. 34 + 2x = 180
Answers
Explanation: an isosceles triangle has 2 sides that are the same, so if the base angles are both 34° then you can multiply that by 2 to get 68°. After that you know that you're still missing one of the angles so that missing angle is x. The equation you can set up to solve for x is the following: 68° + x° = 180°
Hope this helped! :)
A box of facial tissue has a volume of 180 cubic inches. What is the width of the box if the height was 4 inches, and the length was 9 inches?
Answers
Answer:
The width of the box is 5 in
Step-by-step explanation:
the formula for the volume of a rectangular box of length L, width W and height H is V = L*W*H. Here we know V, L and H and want to find W. Solving this equation for W, we get W = V/(LH).
With V = 180 in^3, H = 4 in and L = 9 in, W comes out to be
180 in^3
W = ------------------ = 5 in
(4 in)(9 in)
The width of the box is 5 in
Answer:
Solution :-We have
[tex] \begin{cases} \sf Volume = \frak{480 \: cu \: cm}\\ \sf Length = \frak{4 \: in} \\ \sf Height = \frak{4 \: in}\end{cases}[/tex]
Volume = lbh
180 = 9 × b × 4
180 = 36b
180/36 = b
5 = b
Therefore,
Breadth is 5 inKayla works at a coffee shop. Yesterday she earned $6.25 an hour plus $8.75 in tips. Let x represent the number of hours worked and y represent the total amount earned. Fill in each blank. NO CAPS NO SPACES Slope: Initial value: Equation: y=
Answers
Answer:
y = 6.25x + 8.75
Step-by-step explanation:
Kayla works at a coffee shop. Yesterday she earned $6.25 an hour plus $8.75 in tips.
Let x represent the number of hours worked and y represent the total amount earned.
We have,
Net tip = $8.75
She earned $6.25 per hour.
Initial value = 8.75
So,
Total amount earned, y = 6.25x + 8.75
Hence, this is the required solution.
Wolverine is three years older than Storm Cyclops is two years younger than Storm. The
sum of their age is 106. How old are each of them
Answers
Answer:
Storm is 35, Cyclops is 33 and Wolverine is 38.
Step-by-step explanation:
W, S and C represent the agres of Wolverine, Storm and Cyclops.
W = S + 3
C = S - 2
W + S + C = 106
Making the indicated substitutions, we get:
(S + 3) + S + (S - 2) = 106
Combining like terms:
3S + 1 = 106, and 3S = 105. Thus,
S = 35, C = 35 - 2, and W = S + 3.
Storm is 35, Cyclops is 33 and Wolverine is 38.
¿Can i get the answer?
Answers
Answer:
15.7
Step-by-step explanation:
5 x 3.14(pi) = 15.7
State of the given binomial is a factor of the given polynomial
Answers
Answer:
B no
Step-by-step explanation:
If (n - 10) is a factor then if the polynomial equals zero when evaluated for 10 it is a factor
10³ - 17(10)² + 61(10) + 92
= 1000 - 1700 + 610 + 92
= 2 ≠ 0
Then ( n - 10) is not a factor of the polynomial