Question

find ( mangle d ).
triangle with right angle at c, side dc = 7.2, hypotenuse db = 9, vertices d, c, b
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle d = square^circ )

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle DCB \) with \( \angle C = 90^{\circ} \), \( DC = 7.2 \), and hypotenuse \( DB=9 \). We can use the cosine function to find \( \angle D \) because \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \), where the adjacent side to \( \angle D \) is \( DC \) and the hypotenuse is \( DB \). So \( \cos(\angle D)=\frac{DC}{DB}=\frac{7.2}{9} \).

Step2: Calculate the angle

First, calculate \( \frac{7.2}{9}=0.8 \). Then, to find \( \angle D \), we take the inverse cosine (arccos) of \( 0.8 \). Using a calculator, \( \angle D=\arccos(0.8) \). Calculating this, we get \( \angle D\approx36.9^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 36.9 \)