Question

find the measure of angle d in degrees. round to two decimal places as necessary. draw 12 d 16 show your work here d =

Explanation:

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

In the right triangle, the hypotenuse (opposite the right angle) is \( 16 \), and the adjacent side to angle \( d \) is \( 12 \). We use the cosine function, which is defined as \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \). So for angle \( d \), \( \cos(d) = \frac{12}{16} \).

Step2: Solve for \( d \)

To find \( d \), we take the inverse cosine (arccos) of \( \frac{12}{16} \). First, simplify \( \frac{12}{16} = \frac{3}{4} = 0.75 \). Then, \( d = \arccos(0.75) \). Using a calculator to find the arccos of \( 0.75 \) in degrees, we get \( d \approx 41.41^\circ \) (rounded to two decimal places).

Answer:

\( 41.41^\circ \)