Question

find h.
write your answer as a whole number or a decimal. do not round.
h = \boxed{} meters

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle FHG \) and \( \triangle DEG \) are similar (AA similarity, as two angles are equal: right angle and equal marked angles).

Step2: Set up proportion

For similar triangles, \( \frac{FH}{DE}=\frac{HG}{h} \). Substitute \( FH = 45.5 \), \( DE = 65 \), \( HG = 39.2 \):
\( \frac{45.5}{65}=\frac{39.2}{h} \)

Step3: Solve for \( h \)

Cross - multiply: \( 45.5h=65\times39.2 \).
Calculate \( 65\times39.2 = 2548 \).
Then \( h=\frac{2548}{45.5}=56 \).

Answer:

56