which mountains peaks can be seen from Oahu.

Question

Island Distance(Mi) Mountain Height(ft)
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.

Could someone go through the steps to solve this?

I have already done so but I seem to get close but different answers I need to check my work.

Answer 1

Assume that the observer is at sea-level.

The horizontal line is tangent to the earth at Oahu,
distance = 40 miles = 40*5280'=211200'

The radius of the earth is
r=3960 miles=20908800'
and is perpendicular to the horizontal line above.

Hypotenuse
=sqrt(211200²+20908800²)
=2745600√(58)'
Visible height
= hypotenuse - radius of earth
= 1066.64' < 4961
Therefore the said peak is visible.

Answer 2

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 Lanai-hale visible from Oahu?
C) Repeat parts A & B for the other 3 islands
D) Which 3 Mountains are visible from Oahu?
Can someone draw me a diagram and explain to me what to do step by step? please and thank you!!