Find the measurement and round to the nearest tenth.
[Law of Sines]​

Work Shown:

The uppercase letters A,B,C are the angles, while the lowercase counterparts (a,b,c) are the sides opposite those angles. For instance, side b is opposite angle B.

We have this known info:

The ultimate goal is to find side BC, which is opposite angle A. So this is side a.

Now apply the law of sines to solve for 'a'.

sin(A)/a = sin(C)/c

sin(59)/a = sin(15)/10

10*sin(59) = a*sin(15)

a*sin(15) = 10*sin(59)

a = 10*sin(59)/sin(15)

a = 33.1184013279463

Make sure your calculator is in degree mode.

This rounds to the nearest tenth to get a = 33.1 which is the approximate length of side BC.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.