Question

Triangle FGH has the following measures: m∠G=47∘, f=30.2, and m∠H=79∘. What is the length of side g?36.654.027.331.5

Answer 1

The Solution:

Given:

Represent the given information in a diagram:

Step 1:

Find the measure of angle F.

By the sum of angles in a triangle, we have that:

$\begin{gathered} \angle F=180-(\angle G+\angle H) \\ \\ \angle F=180(47+79)=180-126=54^o \end{gathered}$

Step 2:

Find the length of g.

By applying the sine law:

$\begin{gathered} \frac{f}{\sin F}=\frac{g}{\sin G} \\ \\ \frac{30.2}{\sin54}=\frac{g}{\sin47} \end{gathered}$

Cross multiply,

$g=\frac{30.2\sin47}{\sin54}=27.3009\approx27.3$

Therefore, the correct answer is [option 4]