Question

find m∠f.

write your answer as an integer or as a decimal rounded to the nearest tenth.

m∠f =
submit

Explanation:

Step1: Identify triangle type

Triangle \( FHG \) is right - angled at \( H \), so we can use trigonometric ratios. We know the lengths of the two legs: \( FH = 5.8 \) and \( HG=5.4 \). To find \( m\angle F \), 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 \( \angle F \), the opposite side is \( HG = 5.4 \) and the adjacent side is \( FH=5.8 \).

Step2: Apply tangent formula

The formula for the tangent of an angle \( \theta \) in a right - triangle is \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle F \), let \( \theta = \angle F \), then \( \tan(\angle F)=\frac{HG}{FH}=\frac{5.4}{5.8}\approx0.931 \).

Step3: Find the angle

To find \( \angle F \), we take the arctangent (inverse tangent) of \( 0.931 \). So \( \angle F=\arctan(0.931) \). Using a calculator, \( \arctan(0.931)\approx43.0^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 43.0 \)