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, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In right - triangle $GJH$, if $\theta = \angle JGH$, the side opposite to $\angle JGH$ is $JH$ and the hypotenuse is $GH$.

Step2: Calculate the sine of $\angle JGH$

We know that $JH = 2$ cm and $GH=6$ cm. So, $\sin(\angle JGH)=\frac{JH}{GH}=\frac{2}{6}=\frac{1}{3}$.

Step3: Find the angle measure

To find the measure of $\angle JGH$, we use the inverse - sine function. $\angle JGH=\sin^{- 1}(\frac{1}{3})$. Using a calculator, $\sin^{-1}(\frac{1}{3})\approx19.5^{\circ}$.

Answer:

$19.5^{\circ}$