Question

calculate the given angle, to the nearest degree.
?
51
35
a. 43°
b. 56°
c. 34°
d. 47°

Explanation:

Step1: Identify trigonometric ratio

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, the side opposite the unknown angle is 35 and the hypotenuse is 51. So, $\sin\theta=\frac{35}{51}$.

Step2: Calculate the angle

$\theta = \sin^{- 1}(\frac{35}{51})$. Using a calculator, $\theta=\sin^{-1}(0.686275)\approx43^{\circ}$.

Answer:

A. $43^{\circ}$