Question

You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height. The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees. This forms a right triangle. (a) What is the measure of the other acute angle?(b) What is the height of the tree?

Answer 1

(a)
`55^o`

(b)
`350.1ft`

Explanation:

The sum of the angles inside a triangle must be 180°, but from the right angle we already have 90°, so the sum of the two acute angles is 90°, then:

`90^o-35^o=55^o`

Let
`s` be the length of the shadow and
`h` the height of the three, so tan(35) is

`tan(35^o)=(h)/(s)`

Solving that last equation for h:

`h=s*tan(35)=500(0.7002)=350.1ft`