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: Define variables and set proportion

Let $h$ = height of building. The ratio of corresponding sides is equal:
$\frac{\text{Height of person}}{\text{Height of building}} = \frac{\text{Distance } AB}{\text{Distance } AC}$
First calculate $AC = AB + BC = 8 + 42 = 50$ feet.
Proportion: $\frac{6}{h} = \frac{8}{50}$

Step3: Solve for $h$

Cross-multiply to isolate $h$:
$h = \frac{6 \times 50}{8}$

Step4: Compute final value

$h = \frac{300}{8} = 37.5$

Answer:

37.5 feet