Question

Two angles of a triangle measure 48° and 97°. If the longest side is 12 cm, find the length of the shortest side to the nearest tenth.

A) 5.8 cm
B) 6.9 cm
C) 8.1 cm
D) 9.0 cm

Answer 1

B) 6.9 cm

Explanation:

The remaining angle is the smallest, 180° -48° -97° = 35°. The shortest side is opposite this angle. The Law of Sines tells you its length is ...

short side = (longest side)·(sin(smallest angle)/sin(largest angle))

= (12 cm)sin(35°)/sin(97°) ≈ 6.9 cm

The shortest side is about 6.9 cm.