Question

While hiking on a level path toward Colorado's front range, Otis Evens determines that the angle of elevation to the top of Long Peck is 30 degrees. Moving 1000ft closer to the mountain, Otis determines the angle to be 35 degrees. How mush higher is the top of Long's Peak than Otis's elevation?

Answer 1

Does this help at all?

Answer 2

Tan 30 = ?/x

? = x*Tan (30)

Tan 35 = ?/(x-1000)

Tan 35 = (x*Tan(30))/(x-1000)

x*Tan(35) - 1000*Tan(35) = x*Tan(30)

-1000*Tan(35) = x*Tan(30) - x*Tan(35)

-1000*Tan(35) = x(Tan(30)-Tan(35))

x = (-1000 Tan(35))/(Tan(30)-Tan(35))

x = approx. 5699.36

plug x back in to find ?

Tan 30 = ?/(5699.36)

? = (5699.36)(Tan(30))

? = 3290.5