Question

Your friend is trying to calculate the height of a nearby oak tree. You tell him that you learned how to use similar triangles in Geometry class. You tell your friend to measure his height (75 inches) and you measure the length of his shadow (48 inches). Both of you measure the length of the tree’s shadow (38 feet). How tall is the tree (in feet)? Round to the nearest hundredth.

Answer 1

The height of the tree is 59.38 feet.

Explanation:

It is given that the height of friend is 75 inches and the length of his shadow is 48 inches.

The ratio of height and shadow of friend is

`(height)/(shadow)=(75)/(48)`

Let the length of the tree in feet is x.

The length of the tree’s shadow is 38 feet. The ratios of height and shadow of tree is

`(height)/(shadow)=(x)/(38)`

Using similar triangles property the ratio of height and shadow is same for both objects.

`(75)/(48)=(x)/(38)`

Multiply both sides by 38.

`(75)/(48)* 38=x`

`(475)/(8)=x`

`x=59.375`

`x\approx 59.38`

Therefore the height of the tree is 59.38 feet.