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 the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Let \(\theta = \angle JGH\). The side opposite to \(\angle JGH\) is \(JH\) and the hypotenuse is \(GH\).
So, \(\sin\angle JGH=\frac{JH}{GH}\).

Step2: Substitute the given values

Given \(JH = 2\mathrm{cm}\) and \(GH=6\mathrm{cm}\). Then \(\sin\angle JGH=\frac{2}{6}=\frac{1}{3}\).

Step3: Find the angle using the inverse sine function

\(\angle JGH=\sin^{- 1}(\frac{1}{3})\). Using a calculator, \(\sin^{-1}(\frac{1}{3})\approx19.5^{\circ}\) (since \(\sin(19.5^{\circ})\approx0.333\)).

Answer:

\(19.5^{\circ}\) (the second option)