Given angles 0.33029 rads and 1.176 rads, with included side 160 meters long. How long are the other sides?

Question

Please help

Answer 1

First, let's find the third angle of that triangle. I think it's easier to think about angles in terms of degrees, so I'm going to convert those given angles to degrees...

 

(0.33029)(180)/π = 18.92°

(1.176)(180)/π = 67.38°

 

So, the third angle is 180 - (18.92 + 67.38) = 180 - 86.3 = 93.7°.

 

 

 

Let's call the 18.92° angle A, the 67.38° angle B, and the 93.7° angle C. The side opposite A will be a, the side opposite B will be b, and the 160 m side will be c.

 

Now, we'll use the Law of Sines to find the lengths of sides a and b:

 

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

sin(18.92)/a = sin(93.7)/160

160(sin(18.92)) = a(sin(93.7))

51.88 = a(0.998)

51.99 = a

 

Side a is approximately 52 meters long.

 

sin(B)/b = sin(C)/c

sin(67.38)/b = sin(93.7)/160

160(sin(67.38)) = b(sin(93.7))

147.69 = b(0.998)

147.998 = b

 

Side b is approximately 148 meters long.