Question

A person standing at the top of Mountain Rainier would be approximately 2.7 mi high. The radius of earth is 3959 mi. What is the distance to the horizon from this point? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answer 1

the answer is 146.2

Answer 2

Answer:
`146.2\text{ miles}`

Explanation:

Given: The approximate height of Mountain Rainier h= 2.7 miles

The radius of earth = 3959 miles.

Let d be the distance to the horizon from this point.

We know that the line of sight to the horizon , the radius at the horizon and the radius at the mountain from a right angle triangle.

Therefore, by Pythagoras's theorem we have

`d=√((R+h)^2 - R^2)\\\\\Rightarrow\ d=√((3959+2.7)^2-(3956)^2)\\\\\Rightarrow\ d=√((3961.7)^2-(3956)^2)\\\\\Rightarrow\ d=√(15695066.89-15673681)\\\\\Rightarrow\ d=√(21385.89)\\\\\Rightarrow\ d=146.23915344\approx146.2\text{ miles}`

Hence, the distance to the horizon from this point=
`146.2\text{ miles}`