find g. write your answer as an integer or as a decimal rounded to the nearest tenth. g =
find g. write your answer as an integer or as a decimal rounded to the nearest tenth. g =
Answer
Explanation:
Step1: Find angle E
The sum of angles in a triangle is 180°. So, $\angle E=180^{\circ}-41^{\circ}-24^{\circ}=115^{\circ}$.
Step2: Use the Law of Sines
The Law of Sines states that $\frac{g}{\sin G}=\frac{15}{\sin E}$. We know $G = 41^{\circ}$, $E=115^{\circ}$ and the side opposite $E$ is 15. So, $g=\frac{15\times\sin41^{\circ}}{\sin115^{\circ}}$.
Step3: Calculate the value of g
$\sin41^{\circ}\approx0.656$, $\sin115^{\circ}\approx0.906$. Then $g=\frac{15\times0.656}{0.906}=\frac{9.84}{0.906}\approx10.9$.
Answer:
$10.9$