Question

in △fgh, h = 10, m∠f = 65°, and m∠g = 35°. what is the length of g? use the law of sines to find the answer.
5.8 units
6.7 units
9.2 units
9.8 units

Explanation:

Answer:

First, find \(m\angle H=180^{\circ}-65^{\circ}-35^{\circ}=80^{\circ}\). By the law of sines \(\frac{g}{\sin G}=\frac{h}{\sin H}\), so \(g = \frac{h\sin G}{\sin H}=\frac{10\times\sin35^{\circ}}{\sin80^{\circ}}\approx5.8\) units. So the answer is 5.8 units.