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?

Answer 1

Looks like the ambiguous case of the sine law.
let the angle opposite the 90 be Ø
sinØ/90 = sin 59/80
sinØ =.9643
Ø = 74.6 or 105.4°

so the third angle is
46.4° or 15.6°

now use the sine law for each case to find the two different possibilities for the third side.

There are two triangles possible with your given information, try sketching both using my answers.

Answer 2

Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter. Show your work.