Question

law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ in $\triangle fgh$, $h = 10$, $mangle f=65^{circ}$, and $mangle g = 35^{circ}$. 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:

Step1: Find angle H

$m\angle H = 180^\circ - 65^\circ - 35^\circ = 80^\circ$

Step2: Apply Law of Sines

$\frac{\sin(G)}{g} = \frac{\sin(H)}{h} \implies g = \frac{h \cdot \sin(G)}{\sin(H)}$

Step3: Substitute values

$g = \frac{10 \cdot \sin(35^\circ)}{\sin(80^\circ)} \approx \frac{10 \cdot 0.5736}{0.9848} \approx 5.8$

Answer:

A. 5.8 units