find gh. write your answer as an integer or as a decimal rounded to the nearest tenth. gh =
find gh. write your answer as an integer or as a decimal rounded to the nearest tenth. gh =
Answer
Explanation:
Step1: Identify the trig - ratio
In right - triangle $GIH$, we know the angle $\angle G = 22^{\circ}$ and the side $IH = 2$. We want to find the hypotenuse $GH$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin G=\frac{IH}{GH}$.
Step2: Rearrange the formula
From $\sin G=\frac{IH}{GH}$, we can rewrite it as $GH=\frac{IH}{\sin G}$.
Step3: Substitute the values
We know that $G = 22^{\circ}$ and $IH = 2$. So $GH=\frac{2}{\sin22^{\circ}}$. Since $\sin22^{\circ}\approx0.3746$, then $GH=\frac{2}{0.3746}\approx5.3$.
Answer:
$5.3$