Question

You are on level ground in the late afternoon. the sun is at angle of elevation of 20 degrees. a tree casts a 200 feet long shadow. the height of the tree is

Answer 1

72.8 ft

Explanation:

In order to solve this, you have to use the law of sines, the shadow cast would be the opp side to the 20º angle that you the have over the tree and the height of the tree so we would use tan to solve this:

`tan=(opp)/(adj)`

So we clear Height from the equation:

`tan20=(Height)/(200)\\ Height=200ft*tan20 \\Height=200ft*0.36397\\Height=72,8 ft`

So now we know that the height of the tree would be 72,8 feet.

Answer 2

tan(elevation angle) = (tree height)/(shadow length)
tan(20°) = (tree height)/(200 ft)
(tree height) = (200 ft)*tan(20°) ≈ 72.8 ft