Question

Two of the sides of a triangular lot have lengths of 90 feet and 80 feet. If the angle opposite the 80-foot side is 59°, what is the length of the third side of the lot to the nearest tenth of a foot?

A.



10 ft


B.



65.1 ft


C.



67.5 ft


D.



57.9 ft

Answer 1

67.5!

Answer 2

how?

Answer 3

You need to apply the Sine Rule twice, firstly to get te angle opposite the 90 foot length. Call this angle A.

Now Sin A/90 = sin 59/80 which gives Sin A = 90 x Sin 59/80 hence A = 74.647....

So the third angle in the triangle is 180 - 59 - 74.647... = 46.3529....

Call the third length c. Now c/Sin 46.3529... = 80/ Sin 59 so c = 67.53455...

67.5 is the answer.