Answer: 33.1
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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:
- A = 59 degrees
- C = 15 degrees
- c = 10 yards
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.
