Question

find m∠f.
h
2
g
1
f
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠f =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right triangle \( \triangle FHG \) with \( \angle H = 90^\circ \), \( FH = 1 \) (opposite to \( \angle G \)), \( HG = 2 \) (adjacent to \( \angle F \)), and we need to find \( m\angle F \). We can use the tangent function: \( \tan(\angle F)=\frac{\text{opposite}}{\text{adjacent}}=\frac{HG}{FH} \).

Step2: Calculate the tangent value

Substitute \( HG = 2 \) and \( FH = 1 \) into the formula: \( \tan(\angle F)=\frac{2}{1} = 2 \).

Step3: Find the angle using arctangent

To find \( \angle F \), we take the arctangent (inverse tangent) of 2: \( \angle F=\arctan(2) \). Using a calculator, \( \arctan(2)\approx 63.4^\circ \) (rounded to the nearest tenth).

Answer:

\( 63.4 \)