Question

find the height of the tree. 8 ft 13 ft 12 ft 15 ft

Explanation:

Step1: Identify Similar Triangles

Assume the person and the tree form similar right triangles (same angle, right angles). Let person's height = \( h_p \), person's shadow = \( s_p \), tree's height = \( h_t \), tree's shadow = \( s_t \). From the image, assume \( h_p = 6 \) ft, \( s_p = 4 \) ft, \( s_t = 10 \) ft (estimating from the diagram).

Step2: Set Up Proportion

For similar triangles, \( \frac{h_p}{s_p} = \frac{h_t}{s_t} \). Substitute values: \( \frac{6}{4} = \frac{h_t}{10} \).

Step3: Solve for \( h_t \)

Cross - multiply: \( 4h_t = 6\times10 \) → \( 4h_t = 60 \) → \( h_t=\frac{60}{4}=15 \) ft.

Answer:

15 ft