Question

1

Crista works for a company that cuts down diseased palm trees before they fall and cause
damage. She must determine the height of the palm tree.
5 ft
6 ft
27 ft
Crista is 5 feet tall and has measured her shadow to be 6 feet long. At the same time, she
measured the tree's shadow to be 27 feet long. What is the height (h) of the palm tree?

Answer 1

To determine the height of the palm tree, we set up a proportion using similar triangles and found that the tree is 22.5 feet tall.

Step-by-step explanation:

Crista, at 5 feet tall, casts a 6-foot long shadow while at the same time, the palm tree has a 27-foot long shadow. To determine the height (h) of the palm tree, we use similar triangles, which are proportional in shape but differ in size. Since Crista's height and shadow form one triangle, and the tree's height and shadow form a similar larger triangle, we set up the proportion:

5 ft (Crista's height) / 6 ft (Crista's shadow) = h (tree's height) / 27 ft (tree's shadow)

We solve for h by finding its cross product:

5 ft × 27 ft = 6 ft × h

135 ft² = 6 ft × h

h = 135 ft² / 6 ft

h = 22.5 ft

Therefore, the palm tree is 22.5 feet tall.