Question

Mark wanted to know how tall the tree in his front yard is. At the same time of day, he measured the length of his shadow and the length of the shadow cast by the tree. Mark, who is 5 feet tall, cast a shadow 10 feet long, and the tree's shadow was 140 feet long. How many feet tall is the tree?Mark wanted to know how tall the tree in his front yard is. At the same time of day, he measured the length of his shadow and the length of the shadow cast by the tree. Mark, who is 5 feet tall, cast a shadow 10 feet long, and the tree's shadow was 140 feet long. How many feet tall is the tree?

Answer 1

Step-by-step explanation:

this creates 2 similar triangles.

that means all the angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

10 × f = 140

f = 140 / 10 = 14

now the same factor applies also to the relation of the heights :

5 × 14 = 70 ft

the tree is 70 ft tall.