Use the Law of Cosines to determine the indicated angle 𝜃 (in degrees) shown in the following figure. (Round your answer to one decimal place.)

Question

A triangle is given.

1. The first side of length 24 is opposite the angle 𝜃. (C)
2. The second side of length 19 is opposite an unlabeled angle.
3. The third side of length 12 is opposite an unlabeled angle.

𝜃 =  ?°

Answer 1

theta = about 98.957

= about 99.0 degrees

rounded off to nearest 10th of a degree

use an online triangle solver or laws of sines and cosines

24^2 = 12^2 + 19^2 -2(12)(19)cosC

solve for C

then use laws of sines to find another angle

then last angle = 180 minus the other 2 angles

Answer 2

Use this form of the law of cosines:

cos A = (b² + c² - a²) / (2bc)

a is the side across from (or opposite to) angle A.

The result is 98.96 degrees, approximately, or 99.0 degrees to one decimal place.

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