Determine the remaining sides and angles of the triangle ABC
what is the measure of angle B
what is the length of side a
what is the length of side b
Answers
Answer:
The measure of angle B is 41.5°
The length of side a is 30.6 feet ⇒ to the nearest tenth
The length of side b is 32.9 feet ⇒ to the nearest tenth
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°In the given Δ ABC
∵ m∠A = 38.1°
∵ m∠C = 100.4°
→ By using the fact above
∵ m∠A + m∠B + m∠C = 180°
∴ 38.1 + m∠B + 100.4 = 180
→ Add the like terms in the left side
∴ 138.5 + m∠B = 180
→ Subtract 138.5 from both sides
∴ m∠B = 41.5°
∴ The measure of angle B is 41.5°
∵ a is the opposite side of ∠A
∵ b is the opposite side of ∠B
∵ c is the opposite side of ∠C
→ By using the sine rule
∴ [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4
→ Substitute them in the sine rule above
∴ [tex]\frac{a}{sin38.1}[/tex] = [tex]\frac{b}{sin41.5}[/tex] = [tex]\frac{48.4}{sin100.4}[/tex]
→ By using cross multiplication between the 1st and the 3rd fractions
∴ a × sin 100.4 = 48.8 × sin 38.1
→ Divide both sides by sin 100.4
∴ a = 30.61429861
∴ The length of side a is 30.6 feet ⇒ to the nearest tenth
→ By using cross multiplication between the 2nd and the 3rd fractions
∴ b × sin 100.4 = 48.8 × sin 41.5
→ Divide both sides by sin 100.4
∴ b = 32.87596206
∴ The length of side b is 32.9 feet ⇒ to the nearest tenth
Related Questions
Help pls if u can pls
Answers
Answer and Step-by-step explanation:
8. HL theorem - Has a right angle and the legs.
9. ASA - Angle A is congruent to angle B because of interior angles theorem, side AM is congruent to side MB because of midpoint theorem, angle AMC is congruent to angle BMD because of vertical angles theorem.
10. SSS - The two sides are congruent, and the hypotenuse is shared, making it congruent.
11. SAS - The two sides are congruent, and the angle between the congruent sides are congruent.
#teamtrees #WAP (Water And Plant)
8. RHS congruence rule
9. SAS congruence rule
10. SSS congruence rule
11. SAS congruence rule
for the first select option:
-MJ or ML or MK or KL
for the second select option:
-congruent or not congruent
for the third select option:
-include or do not include
for the fourth select option:
-congruent or not congruent
giving brainliest !
Answers
Answer:
1.) ML
2.) congruent
3.) include
4.) congruent
A hotel has 22 clean towels and 78 dirty towels. What is the ratio of the number of clean towels to the total number of towels?
Answers
Answer:
22:78
Step-by-step explanation:
lol
10. Which of the following represents a linear function? *
I The area of a square in relation to its side
II The area of a circle in relation to its radius
III The perimeter of a square in relation to its side
IV The circumference of a circle in relation to its diameter
(a) I only
(b) II & III
(c) III & IV
(d) IV only
Answers
algebra help quick lol
Answers
Answer:
Its the top right one
Step-by-step explanation:
Which direction am I going if I drive from Washington DC to Dallas texas
Answers
Answer:
north
Step-by-step explanation:
Find the area of the rectangle.
(8x+5) yards
(8x-5) yards
Answers
Step-by-step explanation: To find the area, we can use the F.O.I.L. method.
Notice that these two binomials are identical except
that one has a plus and one has a minus.
These types of binomials are called conjugates.
If you're asked to F.O.I.L. two conjugates, you can
ignore the outer and inner products,
knowing they will cancel each other out.
So the answer to this problem comes from the product
of the first terms and the product of the last terms.
So our answer is 64x² - 25.
Solve: |x - 4| = 0
Help if can
Answers
Answer:
answer is x=4 I'm pretty sure
Step-by-step explanation:
I used a calculator
Answer:
x=4
Step-by-step explanation:
If you plug 4 in, 4-4=0 and the absolute value will not change anything.
What are the coordinates of the image of triangle ABC after dilation with the center (0,0) and the scale factor of 3?
Answers
Answer:
1.5
Step-by-step explanation:
Joe went shopping for holiday gifts for her family. She has a budget of $150. She has 15 people to purchase a gift for, but also would like to spend $30 on her self. Write and solve an inequality to determine the maximum amount she can spend on her family.
Answers
120 / 15 = $8
(150 - 30) divided by 15 = $8
Only $8 maximum can be spent on each family member
elm st. and spruce st. are parallel what is m<1
Answers
Answer:
The measure is 68
Step-by-step explanation:
180-112 = 68
side alternate exterior (supplementary)
The measure of angle 1 will be equal to 68.
What are supplementary angles?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet. The supplementary angle is defined as the angle having the sum of 180 degrees.
Given that there are two parallel lines intersecting one line at an angle of 112. The angle 1 will be calculated as:-
The angle will be calculated as follows:-
∠1 + 112 = 180
∠1 = 180 - 112 = 68
Therefore, the measure of angle 1 will be equal to 68.
To know more about supplementary angles follow
https://brainly.com/question/2046046
#SPJ5
Which of the following is equal to 51/3?
Answers
Answer:
17 hope this helps
Step-by-step explanation:
Simplify the expression below: (3−13)2+1442−5·2
Answers
Answer:
1412
Step-by-step explanation:
2*(3 - 13) + 1442 - (5 * 2)
Distribute the 2 to the 3 and -13, and multiply 5 and 2 together.
6 - 26 + 1442 - 10
Now simplify the expression by adding and subtracting the terms.
1412 is the answer.
#teamtrees #WAP (Water And Plant)
You earned a 90% on a science test. You answered 18 questions
correctly. How many questions were on the test?
Answers
Answer:
20 questions
Step-by-step explanation:
10 divided by 20 is 0.9 which would be 90%
Suppose your family spent $2438.67 on home energy last year. Estimate the amount spent on heating and cooling, rounded to the nearest hundred.
Answers
Answer:
The answer is "1200".
Step-by-step explanation:
The percentage value for [tex]\frac{heating}{cooling}= (48 \% )[/tex]
So,
[tex]\to 2438.67 \times \frac{48}{100} \\\\\\\to 117,056.16 \times \frac{1}{100}\\\\\to 1170.5616\\\\[/tex]
rounding the value into the nearest hundred =1200
Help Me!! Please. Its important
Answers
Answer:
answer to 3 is
Step-by-step explanation:
1 hour = 0.7
2 hours = 1.4
3 hours = 2.1
4 hours = 2.8
5 hours = 3.5
6 hours = 4.2
7 hours = 4.9
8 hours= 5.6
9 hours= 6.3
10 hours= 7.0
11 hours = 7.7
12 hours =8.4
Chaise's mom buys canned tuna for lunches. The cans are in the shape of a cylinder with the dimensions shown below.
What is the volume of the can of tuna, rounded to the nearest tenth?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answers
Answer:
13.81 in
Step-by-step explanation:
the radius is equal to 1.875 and the height is equal to 1.25 . Put these dimensions into the cylinder volume formula and you get 13.81 inches . (plus i got this question right on one of my tests )
What is 26/15 as a whole number?
Answers
Answer:
1 11/15
Step-by-step explanation:
A 18,000 gallon swimming pool contains 7000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1100 gallons per hour
Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.
Volume of Water in Pool
Answers
Answer:
if you put a point at 5,000 and then another at (20,000, 12)
Step-by-step explanation:
i did the other answer and it was wrong
The graph representing the volume of water in the pool over time is illustrated in the graph.
How to illustrate the graph?The problem can be presented by a simple linear equation:
y =mx + b
where
x is the time (hour)
y is the amount of water in x hours
m is the rate of water being added
b is the initial amount of water
y = 1100x + 7000
Learn more about graphs on:
https://brainly.com/question/19040584
How many integers between 27 and 53 have a remainder of 4 divided by 6
Answers
Answer:
There are 4 integers between 27 and 53 that have a remainder of 4 divided by 6.
Step-by-step explanation:
At first we need to find which integers between 27 and 53 are divisible by 6, which are, respectively:
[tex]A =\{30, 36, 42, 48\}[/tex]
All integers that have a remainder of 4 divided by 6 are found by summing 4 to each element of A, that is:
[tex]A' = \{34,40,46, 52\}[/tex]
There are 4 integers between 27 and 53 that have a remainder of 4 divided by 6.
What is the measure of angle G? Type only the number:
Answers
Answer: 48
Step-by-step explanation:
total of all the degrees of the angles of the triangle is ALWAYS 180
let the measure of angle G be x
180 = 102+30+x
180 = 132+x
x = 48
Please help solve this question
Answers
Answer:
x = 0.59 to the nearest hundredth
Step-by-step explanation:
Look at the attached figure
The equation is 2x + [tex]e^{x}[/tex] = 3The red curve represents the left side of the equationThe blue line represents the right side of the equationThe solution of the equation is the point of intersection of the two graphs∵ There are 5 small squares between every 2 numbers on the x-axis
∴ Each square represents 0.2
∵ There are 5 small squares between every 2 numbers on the y-axis
∴ Each square represents 0.2
∵ The point of intersection between the 2 graphs is nearest to
the 3rd small square after the zero on the x-axis
∵ 0.2 × 3 = 0.6
∴ The x-coordinate of the point is approximately located at 0.59
∴ x = 0.59 to the nearest hundredth
what is 25% of 49,490
Answers
Answer:
12,372.5
Step-by-step explanation:
49,490 * 0.25 = 12,372.5
Answer:
12372.5
Step-by-step explanation:
Multiply 49490 by 25 then divide by 100
Hope it helps
Which of the
following represents
this graph?
A. y = (x+11
B. y = |x-1|
c. y = xl-1
D. y = |x|+1
Answers
Answer:
A. y=|x+1|
Step-by-step explanation:
what I like to use when figuring these out(mainly for homework) is a website called Desmos. You basically just plug in whatever equation/expression in and it will graph it for you. My Algebra teacher even allows me to. So all I did was plug in each equation until it matched the graph presented. Hope this helps!
The equation represented by the graph is y=|x+1|
How to determine the equation?The equation is an absolute value graph
The parent function of an absolute value graph is:
y = |x|
The above function is shifted to the left by 1 unit.
This transformation is represented by y=|x+1|
Hence, the equation represented by the graph is y=|x+1|
Read more about function transformation at:
https://brainly.com/question/17586310
#SPJ2
NEED DONE ASAP PLEASE!!! 25points
Answers
Answer:
b i belive i may be incorrect
Step-by-step explanation:
Answer:
it is the second one :)
Step-by-step explanation:
:)
AYOOOOOOOOOO HELP PLESE WILL GIBE BRAINLIST
Answers
Answer:
15 rooms
Step-by-step explanation:
1:$32 = x:$500
$32×x = 1×$500
x = $500/$32
x = 15, 625
Answer:
Might as well collect the points. I'm the guy from the comments.
Step-by-step explanation:
what is five less than a number is greater than twenty
Answers
Answer:
X = -5
Step-by-step explanation:
"Five less than a number is greater than twenty" represents the inequality (x - 5) > 20
Let a number is 'x'.
Now we will construct the inequality for the given statement.
"Five less than a number" means (x - 5)
And "five less than a number is greater than twenty" will be,
(x - 5) > 20
To simplify this inequality,
Add 5 on both the sides of the inequality,
(x - 5) + 5 > 20 + 5
x > 25
Therefore, five less than a number is greater than twenty is an inequality, (x - 5) > 20
Learn more,
https://brainly.com/question/21507783
Write 1270 in expanded form using exponents
Answers
Step-by-step explanation:
Answer:
[tex]1.270[/tex] × [tex]10^{3}[/tex]
I hope this helps!
The owner of a grocery store wants to mix two kinds of candy together to make 15 lb that he can sell for $5.00 per lb. He wants to use chocolate candies that he sells for $7.00 per lb and sugar candies that he sells for $2.00 per lb. How many pounds of each should the owner use?
_ pounds of chocolate candies
_ pounds of sugar candies
=OWO=
Answers
Answer: 9 pounds of chocolate and 6 pounds of sugar candies
Let's define the variables:
C = pounds of chocolate candies used.
S = pounds of sugar candies used.
We know that he wants to make a total of 15lb, then:
C + S = 15
We also want that the price per pound to be equal to 5$.
This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.
C*$7.00 + $2.00*S = $5.00*15
Then we have a system of equations:
C + S = 15
C*$7.00 + $2.00*S = $5.00*15
To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:
C = 15 - S
now we can replace that in the other equation:
(15 - S)*$7.00 + $2.00*S = $5.00*15
Now we can solve this for S.
$105 - $5.00*S = $75
$105 - $75 = $5.00*S
$30 = $5.00*S
$30/$5 = S = 6
Then there are 6 pounds of sugar candy, and we can use the equation:
C + S = 15
C + 6 = 15
C = 15 - 6 = 9
There are 9 pounds of chocolate candy in the mix.
Step-by-step explanation:
By writing and solving a system of equations, we will see that the owner must use 6 lb of the chocolate candies and 9 lb of the sugar candies.
Let's define two variables:
x = pounds of chocolate candies usedy = pounds of sugar candies used.Then, using the given information, we will have that:
x + y = 15
x*$7.00 + y*$2.00 = $5.00*15
If we isolate x in the first equation we get:
x = 15 - y
Now we can replace that in the second equation to get:
(15 - y)*$7.00 + y*$2.00 = $75
$105 - y*$5.00 = $75
$105 - $75 = y*$5.00
$30 = y*$5.00
$30/$5 = y = 6
So the owner must use 6 pounds of the chocolate candies, and the other 9 pounds of the sugar candies.
If you want to learn more, you can read:
https://brainly.com/question/12895249
Find the Solution of the equation -2x + 7 = 7
Answers
Answer:
x = 0
Step-by-step explanation:
-2 x 0 + 7 = 7
-2 x 0 = 0
0 + 7 = 7