Question

question #13 reference q.14167 in each case, calculate the measure of the indicated angle to the nearest degree.

Explanation:

Step1: Recall cosine - sine - tangent relations

For a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Solve for part a

In the first right - triangle, the side adjacent to the angle $x$ is $40$ and the hypotenuse is $41$. Using the cosine function, $\cos x=\frac{40}{41}$. Then $x = \cos^{- 1}(\frac{40}{41})$. Calculate $\cos^{-1}(\frac{40}{41})\approx14^{\circ}$.

Step3: Solve for part b

In the second right - triangle, the side opposite to the angle $x$ is $24$ and the hypotenuse is $40$. Using the sine function, $\sin x=\frac{24}{40}=0.6$. Then $x=\sin^{-1}(0.6)$. Calculate $\sin^{-1}(0.6)\approx37^{\circ}$.

Step4: Solve for part c

In the third right - triangle, the side opposite to the angle $x$ is $33$ and the side adjacent to the angle $x$ is $46$. Using the tangent function, $\tan x=\frac{33}{46}$. Then $x = \tan^{-1}(\frac{33}{46})$. Calculate $\tan^{-1}(\frac{33}{46})\approx36^{\circ}$.

Answer:

a. $14^{\circ}$
b. $37^{\circ}$
c. $36^{\circ}$