Answer: [tex]146.2\text{ miles}[/tex]
Step-by-step 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
[tex]d=\sqrt{(R+h)^2 - R^2}\\\\\Rightarrow\ d=\sqrt{(3959+2.7)^2-(3956)^2}\\\\\Rightarrow\ d=\sqrt{(3961.7)^2-(3956)^2}\\\\\Rightarrow\ d=\sqrt{15695066.89-15673681}\\\\\Rightarrow\ d=\sqrt{21385.89}\\\\\Rightarrow\ d=146.23915344\approx146.2\text{ miles}[/tex]
Hence, the distance to the horizon from this point= [tex]146.2\text{ miles}[/tex]
