Question

Curtis sees a maple tree and a pine tree in the forest. He knows that the pine tree is 20.68 feet tall. On a sunny day, the shadow of the pine is 4.2 feet long while the maple's shadow is 20.02 feet long. Estimate the height of the maple tree.

Answer 1

44.9 here you go it’s pretty easy

Answer 2

The height of the maple is 98.6 feet

Explanation:

Similar Triangles

The triangles formed by each tree's height, their shadow, and the projection of their shadow in the ground are right and similar triangles since the sun has the same elevation at the same time in the same place. It's shown in the image attached.

Curtis sees a maple tree of unknown height Hm and a pine tree of height Hp=20.68 feet. He also measures the projection of the shadow of the pine of Xp=4.2 feet and the same measure of the maple of Xm=20.02 feet.

Since both triangles are similar, the proportion between their sides is equal, thus:

`\displaystyle (Hm)/(Hp)=(Xm)/(Xp)`

Solving for Hm:

`\displaystyle Hm=(Xm*Hp)/(Xp)`

`\displaystyle Hm=(20.02*20.68)/(4.2)`

Hm = 98.6 feet

The height of the maple is 98.6 feet