Question

find m∠g.
f
3.5
5.9
g
h
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠g = °

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle FGH \) with \( \angle F = 90^\circ \), we know the opposite side to \( \angle G \) is \( FH = 5.9 \) and the adjacent side to \( \angle G \) is \( FG = 3.5 \). We use the tangent ratio: \( \tan(\angle G) = \frac{\text{opposite}}{\text{adjacent}} = \frac{FH}{FG} \).

Step2: Calculate the tangent value

Substitute the values: \( \tan(\angle G) = \frac{5.9}{3.5} \approx 1.6857 \).

Step3: Find the angle

Take the arctangent (inverse tangent) of \( 1.6857 \): \( \angle G = \arctan(1.6857) \). Using a calculator, \( \angle G \approx 59.4^\circ \) (rounded to the nearest tenth).

Answer:

\( 59.4 \)