SOLUTION: You are approaching the island of Hawaii in a small boat. The highest point on Hawaii is Mauna Loa at 13,677 feet. You see it just barely above the horizon. The radius of Earth is

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: You are approaching the island of Hawaii in a small boat. The highest point on Hawaii is Mauna Loa at 13,677 feet. You see it just barely above the horizon. The radius of Earth is       Log On


   

Question 18886: You are approaching the island of Hawaii in a small boat. The highest point on Hawaii is Mauna Loa at 13,677 feet. You see it just barely above the horizon. The radius of Earth is 3,963 miles. Ignoring atmospheric effects, you figure that you are miles in a straight line from the top of Mauna Loa.

Answer by tjnw79(57) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a picture of a right triangle where one short side is the unknown distance D, and the other is the radius of earth, R . The long side is the radius of earth plus the height of the mountain, R+H where R=3963 miles and H=13,677 feet. Of course we need to use consistent units, and so we convert the height of the mountain to h=%2813677%29%2F%285280%29 miles. The Pythagorean Theorem tell us that %28R%5E2%29%2B%28D%5E2%29=%28R%2BH%29%5E2
We need to know D. Expanding on the right and subtracting R%5E2 on both sides gives the equation D%5E2=R%5E2%2B2RH%2BH%5E2-R%5E2=RH%2BH%5E2
Other wise as D=sqrt%282RH%2BH%5E2%29

Plugging in the values we are given yields D=143.31 miles