Answer:
The height of Mount Rushmore is [tex]560.18\ ft[/tex]
Step-by-step explanation:
we know that
[tex]tan(48\°)=(x+60)/y[/tex]
[tex]y=(x+60)/tan(48\°)[/tex] -----> equation A
[tex]tan(44.76\°)=x/y[/tex]
[tex]y=x/tan(44.76\°)[/tex] -----> equation B
equate equation A and equation B and solve for x
[tex](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[/tex]
Find the height of Mount Rushmore
The height is equal to
[tex]x+60=500.18+60=560.18\ ft[/tex]
