Math Grade 12
posted by Vanessa on .
So the question is basically asking which mountains peaks can be seen from Oahu.
Island Distance(Mi) Mountain Height(ft)
Lanai  65  Lanaihale  3,370
Maui  110  Haleakala  10,023
Hawaii  190  Mauna Kea  13,796
Molokai  40  Kamakou  4,961
A) Radius of earth= 3960 mi.
Determine angle formed at the center of the earth.
B) Determine length of the hypotenuse.
Is Lanaihale visible from Oahu?
C) Repeat parts A & B for the other 3 islands
D) Which 3 Mountains are visible from Oahu?
Can someone please draw a diagram and explain to me where the angle formed at the center of the earth and hypotenuse please? I'm really despearate to understand this problem! It's due on Monday! please help! xoxoxo <3

If you draw a line from a point above the surface, to the horizon, the angle where the radius meets the point on the horizon is a right angle, because the line is tangent to the surface of the earth.
So, if you have a point x km above the surface, and the radius of the earth is r km, and the distance from the point to the horizon is d km,
r^2 + d^2 = (r+x)^2
If you need to work with the angle θ at the center of the earth,
sinθ = d/(r+x)
tanθ = d/r 
if the first three terms in the expansion of (1+ax)^n in ascending powers
of x are 1+12x+64x^2 find n and a