1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
beks73 [17]
2 years ago
15

Triangle ABC has side lengths a= 24, b= 40, and c= 55. What is the measure of angle C? 83.6° 116.2° 23.0° 40.7°

Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
5 0
<h3>Answer:  116.2°</h3>

Work Shown:

c^2 = a^2 + b^2 - 2ab\cos(C)\\\\55^2 = 24^2 + 40^2 - 2*24*40\cos(C)\\\\3025 = 576 + 1600 - 1920\cos(C)\\\\3025 = 2176 - 1920\cos(C)\\\\3025 - 2176  = -1920\cos(C)\\\\849  = -1920\cos(C)\\\\-1920\cos(C) = 849\\\\\cos(C) = (849)/(-1920)\\\\\cos(C) \approx -0.4421875\\\\C \approx \cos^{-1}(-0.4421875)\\\\C \approx 116.243535748231^{\circ}\\\\C \approx 116.2^{\circ}\\\\

The first equation is one of the three variations for the Law of Cosines.

Make sure your calculator is in degree mode.

You might be interested in
A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)
stiks02 [169]

Answer:  82 sq. units .

Step-by-step explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB =\sqrt{(9+1)^2+(-1-7)^2} units  [By distance formula : \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]

=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41} units

Width = BC = \sqrt{(-1+5)^2+(7-2)^2} units

=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}

Area = length x width

= 2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}

Hence, the  area of the rectangle is 82 sq. units .

7 0
3 years ago
Divide 56 in a ratio of 5:3
Goshia [24]
There are 5 "parts" and 3 "parts"; which total "8 parts" (5 + 3 = 8); so, each part must be 56/8 = 7. so each part must be 56/7 = 8 
<span>5 x 7 is 35</span>
<span>3 x 7 is 21 </span>
___________
So the answer is 35:21 .
6 0
3 years ago
Whole number 6 is equal to ?/3
Ugo [173]

Step-by-step explanation:

That means 6/3 is equivalent to 2 wholes! When the numerator is divisible by the denominator, the fraction is equivalent a whole number. If the numerator is equal to the denominator, you will always have one whole, or 1.

5 0
2 years ago
Need a quick answer please
galben [10]

Answer: angle 1: 62 degrees, angle 2:45 degrees, angle 3: 24 degrees

Step-by-step explanation:

7 0
3 years ago
In how many ways can a gymnastics team of 4 be chosen from 9 gymnasts? Type a numerical answer in the space provided. Do not typ
vovangra [49]
There are 126 ways to choose a team of 4 gymnasts from a set of 9 gymnasts.
4 0
3 years ago
Other questions:
  • Which of the following side lengths can form a triangle?
    15·2 answers
  • A table of equivalent ratios is shown. One value is missing from the table.
    10·2 answers
  • What is the circumference of the circle of a diameter of 12​
    15·2 answers
  • Please help me finish this problem of pythagorean theorem model.​
    5·1 answer
  • I need to find the length of AB.<br><br><br><br>HELP​
    5·2 answers
  • Which definition best describes vertical angles?
    15·1 answer
  • Could someone answer these problems ?
    14·2 answers
  • I need help pls :) &lt;3
    8·1 answer
  • WILL MARK BRAINLEIST!!
    10·2 answers
  • Which number has a 5 in the hundredths place?<br><br> A-54.87 <br> B-4.75 <br> C-32.59
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!