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.
$\bigcirc$ 5.8 units
$\bigcirc$ 6.7 units
$\bigcirc$ 9.2 units
$\bigcirc$ 9.8 units

Explanation:

Step1: Find ∠H

The sum of angles in a triangle is $180^\circ$.
$m\angle H = 180^\circ - 65^\circ - 35^\circ = 80^\circ$

Step2: Apply Law of Sines

Relate $g$, $h$, $\angle G$, $\angle H$.
$\frac{g}{\sin(G)} = \frac{h}{\sin(H)}$

Step3: Solve for $g$

Substitute values: $h=10$, $\sin(35^\circ)\approx0.5736$, $\sin(80^\circ)\approx0.9848$
$g = \frac{10 \times \sin(35^\circ)}{\sin(80^\circ)} \approx \frac{10 \times 0.5736}{0.9848} \approx 5.8$

Answer:

5.8 units