elis8haelleeno
Answered

the summit of Mt. McKinley is about 20,320 feet above sea level. Earth's radius is about 3950 miles. To the nearest mile,what is the distance from the summit to the horizon?


f)67mi

g)174mi

h)1633mi

j)3950mi

Verified Answer :

You have to convert everything into miles and then draw the tangent line that goes from the peak of the mountain to the horizon.  That can form a right triangle since tangent lines are perpendicular to the radius at the point they touch the circle.  then you can solve for the horizon which is one of the legs of the right triangle.  when you do everything it should end up being 174 miles.  I will attach my work so you can try to decipher what to do.

I hope this helps.

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varshamittal029

The distance between the summit and horizon is 174miles.

What is Pythagoras Theorem?

The Pythagoras Theorem implies that in a right-angle triangle, the square of the value of hypotenuse is the sum of square of the value of other two sides of right-angle triangle.

According to asked question

Height of the summit of Mt. McKinley = 20320 feet= 20320/5280 mile=3.85 miles

Radius of earth = 3950 miles

From the below figure, it is obvious that

AB=h=3.85 miles

OB=OC=r=3950 miles

OA=OB+BA=3950+3.85=3953.85 miles

The distance between the summit and horizon is d

So ΔOAC is a right-angle triangle.

So using the Pythagoras theorem,

OC²+CA²=OA²

⇒CA²=OA²-OC²

⇒d²=OA²-r²

⇒d²=(3953.85)²-(3950)²=30417.84

⇒d=√30417.84=174.4miles≅174 miles

Therefore, the distance between the summit and horizon is 174miles.

Learn more about the Pythagoras theorem

Here: https://brainly.com/question/343682

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View image varshamittal029

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