Question

the length of the hypotenuse, line segment gh, in triangle gjh measures 6 cm. line segment jh measures 2 cm. which is the approximate measure of angle jgh? 18.4° 19.5° 70.5° 71.6°

Explanation:

Step1: Recall sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, for $\angle{JGH}$, the opposite side to $\angle{JGH}$ is $JH$ and the hypotenuse is $GH$.
Let $\theta = \angle{JGH}$, then $\sin\theta=\frac{JH}{GH}$.

Step2: Substitute the given values

Given $JH = 2$ cm and $GH=6$ cm. So, $\sin\theta=\frac{2}{6}=\frac{1}{3}$.

Step3: Find the angle

We know that $\theta=\sin^{- 1}(\frac{1}{3})$. Using a calculator, $\sin^{-1}(\frac{1}{3})\approx19.5^{\circ}$.

Answer:

B. $19.5^{\circ}$