Question

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

Explanation:

Step1: Identify triangle type

Triangle \( \triangle GFH \) is right - angled at \( F \), so we can use trigonometric ratios. We know that in a right - triangle, \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle H \), the opposite side to \( \angle H \) is \( GF = 1 \) and the adjacent side is \( FH=2 \).

Step2: Apply tangent ratio

We use the formula \( \tan(m\angle H)=\frac{GF}{FH} \). Substituting \( GF = 1 \) and \( FH = 2 \), we get \( \tan(m\angle H)=\frac{1}{2}=0.5 \).

Step3: Find the angle

To find \( m\angle H \), we take the arctangent (inverse tangent) of \( 0.5 \). So \( m\angle H=\arctan(0.5) \). Using a calculator, \( \arctan(0.5)\approx26.6^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 26.6 \)