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°

Answer 1

Answer:

b. 19.5

Step-by-step explanation:

Answer 2

The approximate measure of angle JGH is 70.529°.

Analysis of a right triangle

According to this question, we have a right triangle in which lengths of its hypotenuse ($GH$), in centimetres, and one leg ($JH$) are known and we must determine the measure of an angle ($m\angle JGH$), in degrees. A representation of this triangle is included in the image attached below.

By trigonometry we have the following expression for the required angle:

$\cos m\angle GJH = \frac{HJ}{GH}$ (1)

($HJ = 2$, $GH = 6$)

$m \angle GJH = \cos ^{-1} \frac{2}{6}$

$m \angle GJH \approx 70.529^{\circ}$

The approximate measure of angle JGH is 70.529°. $\blacksquare$

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