Question

find the measure of angle d in degrees. round to two decimal places as necessary.

Explanation:

Step1: Identify the sides relative to angle \( d \)

In the right triangle, the side opposite angle \( d \) is \( 8 \), and the hypotenuse is \( 32 \). We use the sine function, which is defined as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(d) = \frac{8}{32} \).

Step2: Simplify the fraction

Simplify \( \frac{8}{32} \) to \( \frac{1}{4} = 0.25 \).

Step3: Find the angle using inverse sine

To find \( d \), we take the inverse sine (arcsin) of \( 0.25 \). So, \( d = \arcsin(0.25) \). Using a calculator to find the value in degrees and rounding to two decimal places.

Answer:

\( d \approx 14.48^\circ \)