Question

find m∠h.
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠h = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle FHG \) with \( \angle F = 90^{\circ} \), \( FH = 5 \), and \( FG = 8 \). To find \( m\angle H \), we can use the tangent function. The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For \( \angle H \), the opposite side is \( FG = 8 \) and the adjacent side is \( FH = 5 \). So, \( \tan(\angle H)=\frac{opposite}{adjacent}=\frac{FG}{FH}=\frac{8}{5} \).

Step2: Calculate the angle

We know that if \( \tan(\theta)=\frac{8}{5} \), then \( \theta=\arctan(\frac{8}{5}) \). Using a calculator, we first calculate \( \frac{8}{5}=1.6 \). Then we find \( \arctan(1.6) \). Using a calculator (make sure it is in degree mode), \( \arctan(1.6)\approx58.0^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 58.0 \)