Mike wants to work out the height of a tree which has a fence around it. From A he sees that the angle of elevation of the top is 19° From B, 18m closer, the angle of elevation is 32° Workout the height of the tree
Answers
Answer: 13.8 m
Step-by-step explanation:
Given
From point A, angle of elevation is [tex]19^{\circ}[/tex]
From point B which is 18 m closer, it changes to [tex]32^{\circ}[/tex]
Suppose the height of tree is h
From figure, we can write
[tex]\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}[/tex]
Similarly
[tex]\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m[/tex]
Deduce the value of h
[tex]\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m[/tex]
Thus, the height of the tree is 13.8 m
Related Questions
A container in the shape of this cuboid holds 2 litres of water.
The container has a square base.
Its height is double the length of each edge on its base.
Work out the height of the container, in cm.
Answers
Given:
Volume of cuboid container = 2 litres
The container has a square base.
Its height is double the length of each edge on its base.
To find:
The height of the container.
Solution:
We know that,
1 litre = 1000 cubic cm
2 litre = 2000 cubic cm
Let x be the length of each edge on its base. Then the height of the container is:
[tex]h=2x[/tex]
The volume of a cuboid is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]V=2000,\ l=x,\ w=x,\ h=2x[/tex], we get
[tex]2000=x\times x\times 2x[/tex]
[tex]2000=2x^3[/tex]
Divide both sides by 2.
[tex]1000=x^3[/tex]
Taking cube root on both sides.
[tex]\sqrt[3]{1000}=x[/tex]
[tex]10=x[/tex]
Now, the height of the container is:
[tex]h=2x[/tex]
[tex]h=2(10)[/tex]
[tex]h=20[/tex]
Therefore, the height of the container is 20 cm.
Which expression is equivalent to (x^-6/x^2)^3
1/x
1/x^5
1/x^9
1/x^24
Answers
Step-by-step explanation:
1/x^24 is the correct expression
What is the value of x?
85°
92°
53°
Answers
Answer:
x = 46
Step-by-step explanation:
Vertical angles are equal so call the angle y
85+53 +y =y+ 92+x
Subtract y from each side
85+53 = 92+x
Combine like terms
138 = 92+x
Subtract 92 from each side
138 -92 = 92+x-92
46 =x
Who was the first president of Nigeria
Answers
Answer:
Nnamdi Azikiwe
Step-by-step explanation:
he was the first one
If 4p + 3q + 2r = 3 and -4p - 2q - 2r = 4, then q = ?
(A) 0
(B) 2
(C) 3
(D) 4
(E) 7
Answers
Answer:
E
Step-by-step explanation:
Label the two equations:
4p +3q +2r= 3 -----(1)
-4p -2q -2r= 4 -----(2)
(1) +(2):
4p +3q +2r -4p -2q -2r= 3 +4
Grouping like terms together:
4p -4p +3q -2q +2r -2r= 7
Simplify:
q= 7
Give an example of a function which represents all types of a function. Find the composite function (fog)(x) given that f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}
Answers
Answer:
(fog)(x) = x
Step-by-step explanation:
Composite function:
[tex](f \circ g)(x) = f(g(x))[/tex]
Composite of a function and its inverse.
The composition of a function and it's inverse is the straight line x. So
[tex](f \circ f^{-1})(x) = x[/tex]
f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}
We can see that the x-values in f are the y-values for g, and the y-values for f are the x-values for g, that is, f and g are inverse functions. Thus:
(fog)(x) = x
Find the measurement of the missing side in each right triangle.
Answers
Answer:
12
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
in this case its
[tex]5^{2}[/tex] + [tex]b^{2}[/tex] = [tex]13^{2}[/tex]
25 + [tex]b^{2}[/tex] = 169 subtract 25 from both sides
[tex]b^{2}[/tex] = 144 take square root of each side
b = 12
Answer:
[tex]12[/tex]
Step-by-step explanation:
----------------------------------------
In order to find the missing side of the triangle, we would need to use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex]
So,
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
[tex]b^2=144[/tex]
[tex]b=12[/tex]
--------------------
Hope this helps.
Fill in the blank with the correct response. The slope of the graph of y = -7x is
Answers
Answer:
The slope is -7
Step-by-step explanation:
[tex]y = mx + c[/tex]
The [tex]m[/tex] indicates the slope/gradient of a graph
Answer:
m = -7
Step-by-step explanation:
y = -7x is a typical slope-intercept equation of a straight line. Comparing it to
y = mx + b, we see that the slope, m, is -7 and the y-intercept, b, is 0.
A= P(1+rt)
A= 27 and t=3 solve for r.
Answers
Answer:
(27 - P) / 3P = r
Step-by-step explanation:
A = P(1 + rt)
A = 27
27 = P(1 + 3r)
27 = P + 3Pr
27 - P = 3Pr
(27 - P) / 3P = r
what is 55 degrees in radian measure as a multiple of pi
Answers
Rad=degree/180/π
Rad = 55/180/π
Final answer:
Rad= (11/36)π [this answer is In pi]
Rad= 0.96 [this answers is the simplified version]
A store sells a certain tile for $2 per tile and a pint of paint for $3. A second store sells the same items for $1 per tile and $4 per pint of paint. Ari bought the same number of tiles and pints of paint at both stores, costing him $26 at the first store and $18 at the second store, before tax. Which system of equations can be used to find the number of tiles, x, and the number of pints of paint, y, that Ari bought at each store? A system of equations. 3 x plus 4 y equals 18. X plus 2 y equals 26. A system of equations. X plus 3 y equals 18. 2 x plus 4 y equals 26. A system of equations. 2 x plus 3 y equals 26. X plus 4 y equals 18. A system of equations. 3 x plus 2 y equals 26. 4 x plus y equals 18.
Answers
Answer:
2 x plus 3 y equals 26. X plus 4 y equals 18
Step-by-step explanation:
Number of tiles, = x
Number of pints of paint, = y
Store 1:
Cost per tile = $2 ; cost per pint = $3 ; total cost = $26
Store 2 :
Cost per tile = $1 ; cost per pint = $4 ; total cost = $18
System of equation:
2x + 3y = 26 - - - (1)
x + 4y = 18 - - - - - (2)
The drama club sold $779 worth of tickets to the school play. Student tickets cost $3 apiece and tickets for everyone else cost $5 each. What equation relates the number of student tickets that were sold, s, and the number of other tickets that were sold, t, written in standard form?
s +
t =
Answers
Answer:
3s + 5t = 779
Step-by-step explanation:
Answer:
3 5 779
Step-by-step explanation:
HELP please i need this done by thursday
Answers
f(x-1) - 5
The -1 is the x value
And -5 is the y value.
The vertex formula is a(x-h)^2 + k
This is modified so no ^2.
If you plug -5 in, it would be (x- -5), therefore, it’s positive.
So, (1, -5).
help asap please im failing
Answers
Step-by-step explanation:
The y intercept is when x=0 what is the y value.
When x=0, the y intercept is 1.
b. A gradient is the slope of the line. We need to find the rise and run of the line between two points.
Let use points 0,1 and 1,3
Our y values rise by 2 values and our x values change by 1 value so our slope is
[tex] \frac{2}{1} = 2[/tex]
Answer:
a. At the y-intercept,x=0
This implies the y-intercept=1
b. Taking points (0,1) and (1,3), the gradient of the line is given by (3-1)/(1-0) =2/1 =2
Which is an equivalent form of the expression 1800(1.2)–t?
Answers
Answer:
2160 - t
Step-by-step explanation:
1800(1.2)–t
2160 - t
Please help me find the volume
Answers
Check the picture below.
so we have a pyramid atop and a rectangular prism at its base, so we simply get the volume of each separately and add them up.
[tex]\hspace{34em}|\\ \textit{volume of a pyramid} \\ \cfrac{1}{3}Bh~~ \begin{cases} B=\stackrel{\textit{area of its base}}{6\times 6}\\ h=\stackrel{\textit{its height}}{8} \end{cases} \\\\\\ \cfrac{1}{3}(6\cdot 6)(8)\implies \cfrac{36}{3}\cdot 8\implies 12\cdot 8\implies \underline{96}[/tex]
[tex]\textit{volume of a rectangular prism}\\ Lwh~~ \begin{cases} L=\stackrel{length}{6}\\ w=\stackrel{width}{6}\\ h=\stackrel{height}{4} \end{cases} \\\\\\ 6\cdot 6\cdot 4\implies 36\cdot 4\implies \underline{144} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{volume of the figure}}{96+144\implies 240}~\hfill[/tex]
given that cot(θ)= -√5/3 and cos(θ) < 0, find sin(θ)
Answers
D. 3√14 /14
Step-by-step explanation:
given that cot(θ)= -√5/3 and cos(θ) < 0
cot(θ)= -√5/3 and cos(θ) < 0, the angle should be on quadrant II.
cot(θ)= -√5/3 => x = -√5 , y = 3
h = √(-3)²+5 =√14
so, sin(θ) = y/h = 3/√14 = 3√14 /14
1. Find 3 rational numbers between −1//3 and 1/−5
Answers
Step-by-step explanation:
-1×5 1×3
------ -----
3×5 -5×3
=
-5/15 -3/15
-5/15×4/4 ;
-3/15×4/4
=
-20/60 ;
-12/60
you can write any 8 rational no. between them
please mark as brainliest answer as it will also give you 3 pts
bill has the following test scores in science: 82% 88% and 96%. he hasn’t one more test to take this quarter. if bill wants husband test average to be 90% what score does he need to earn on his last test?
Answers
Answer:
He needs to earn a 94%.
Step-by-step explanation:
[tex]\frac{82+88+96+x}{4} = 90\\ \\ \frac{266+x}{4} =90\\\\ 4(\frac{266+x}{4}) =(90)4\\ \\ 266+x = 360\\ \\ 266+x-266 =360-266\\ \\ \\x = 94[/tex]
He must earn a 94% on his latest test for a test average of 90%
The box-and-whisker plot below represents the number of cars in the airport parking lots. Is there more variability in the number of cars below 120 or above 230? Choose the correct answer and explanation.
Answers
Answer:
report me I want deleted:)
Write an equation to represent the relationship between x and y:
Answers
Answer:
y = 1/3 x - 1
Step-by-step explanation:
use slope formula then substitute an x and y and the m to find b
y=mx+b
[tex]1,6 + 6,13[/tex]
Answers
= 1,6 + 6,13
= 7,73 .
FollowMe? FollowBack.
Answer:
7,73Step-by-step explanation:
1,6
6,13 +
7,73
[tex] \: \: \: [/tex]T= 3x +4y work out the value of T when x = 5 and y = -7
Answers
Answer:
T=-13
Step-by-step explanation:
substitute T=3*5+4*(-7)
the product:T=15-28
the sum:T=-13
Find the 87th term of the arithmetic sequence 12, 0, -12
Answers
Answer:
a(87) = -590
Step-by-step explanation:
Notice how each term of this arithmetic sequence is equal to the sum of the previous term and the common difference, -12.
The general formula a(n) = a(1) + (n - 1)d becomes:
a(n) = 12 - 7(n - 1)
and the 87th term a(87) = 12 - 7(87 - 1), or
a(87) = 12 - 7(86)
a(87) = -590
Ms. Mackey records the number of math problems that each of her students gets correct on a math fact quiz.
The numbers of correct problems on the quizzes for the 15 students are listed below.
Answers
Answer and also explanation:
Use the drawing tool(s) to form the correct answer on the provided plot.
In order to construct a dot plot representing the number of correct problems on each student's quiz, first find the range of the data.
The maximum number of correct problems is 10. The minimum number of correct problems is 2. Therefore, the number of correct problems ranges from 2 to 10.
Next, determine how many students had each number of correct problems in the range.
No. of Correct Problems
0 1 2 3 4 5 6 7 8 9 10
No. of Students 0 0 1 1 2 0 3 2 2 2 2
The number of correct problems, from 0 to 10, will be the values on the number line. The number of students will be the number of dots above each value on the number line.
The dot plot showing the correct number of math problems for Ms. Mackey's students is shown on your question.
Can someone help me with this please ?
Answers
x + 1 = 3/6 x 4 = 2
x = 1
Scale factor = 6 / 4 = 1.5
Ratio of perimeters = 2 : 3
4. x / 21 = 20 / 15
x = 20 / 15 x 21 = 28
Scale factor = 20 / 15 = 4/3
Ratio of perimeters = 3 : 4
Need answer ASAP!!!!
Answers
Answer:
The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.
Step-by-step explanation:
Find the measure of arc CEB
Answers
Answer:
Step-by-step explanation:
Arc CAB through E is just the sum of the 3 minor arcs you are given
Arc CEB = 53 + 79 + 68
Arc CEB = 200
Solve for O pls and thank you
Answers
Answer:
a) 67.4°
Step-by-step explanation:
since this is a right triangle you can use the sine trigonometric ratio of opposite/hypotenuse
sin⁻¹(Ф) = 12/13 which equals 67.4°
20% deposit
5 years to pay
Monthly instalment
R6475,00
how much will he pay after 5 years?
Answers
Answer:
R12,950.00
Step-by-step explanation:
We solve using the formula
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 20%/100 = 0.2 per year.
Solving our equation:
A = 6475(1 + (0.2 × 5)) = 12950
A = R12,950.00
Therefore, the amount he will pay after 5 years is R12,950.00