Question

from a point, a, a line segment includes the top of the head, e, of a person 6 feet tall and the top of the building, d. the ground distance from point a to the person is 8 feet and the ground distance from the person to the building is 42 feet. what is the height of the building?
the height of the building is 37.5 feet.

Explanation:

Step1: Identify similar triangles

Triangles $\triangle ABE$ and $\triangle ACD$ are similar (right triangles sharing $\angle A$).

Step2: Set up proportion

Corresponding sides are proportional: $\frac{\text{Height of person}}{\text{Height of building}} = \frac{AB}{AC}$
First calculate $AC = AB + BC = 8 + 42 = 50$ feet.
Substitute values: $\frac{6}{h} = \frac{8}{50}$

Step3: Solve for building height $h$

Cross-multiply: $8h = 6 \times 50$
$8h = 300$
$h = \frac{300}{8} = 37.5$

Answer:

37.5 feet