Question

Find the height of Mount Rushmore. Show your work.

Answer 1

The height of Mount Rushmore is
`560.18\ ft`

Explanation:

we know that

`tan(48\°)=(x+60)/y`

`y=(x+60)/tan(48\°)` -----> equation A

`tan(44.76\°)=x/y`

`y=x/tan(44.76\°)` -----> equation B

equate equation A and equation B and solve for x

`(x+60)/tan(48\°)=x/tan(44.76\°)\\\\(x)tan(44.76\°)+(60)tan(44.76\°)=(x)tan(48\°)\\\\(x)tan(48\°)-(x)tan(44.76\°)=(60)tan(44.76\°)\\\\x=(60)tan(44.76\°)/(tan(48\°)-tan(44.76\°))\\\\x=500.18\ ft`

Find the height of Mount Rushmore

The height is equal to

`x+60=500.18+60=560.18\ ft`