A pilot is flying a plane 4.5 mi above the earth’s surface.

From the pilot’s viewpoint, what is the distance to the horizon?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

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summertastic1011
Apr 12, 2018

#1**+3 **

a tangent and radius meet at 90 degrees

use Pythagorean theorem

c= 3959mi + 4.5mi

c= 3963.5mi

a^2 = c^2 - b^2

a^2 = 3963.5^2 - 3959^2

a^2 = 35651.25

a= √35651.25

a= 188.8mi (nearest tenth)

lynx7
Apr 12, 2018

#6**0 **

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.

summertastic1011
Apr 12, 2018

#9**+1 **

do we need to find the point at the centre of the earth or the point on the circumfernce of earth?

lynx7
Apr 12, 2018

#13**+3 **

The line of sight to the horizon , the radius at the horizon and the radius at the mountain from a right angle triangle, so Pythagoras's theorem gives

d = sqrt( ((R+h)^2 - R^2)

= sqrt( 2Rh + h^2)

= 146.2mi

lynx7
Apr 12, 2018

#14**+3 **

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?

We can use the Pythagorean Theorem, here

We have a right triangle with a hypotenuse of 3959 + 2.7 = 3961.7 mi

And the radius of the Earth represents one of the legs...so....the distance to the horizon is the other leg and given by :

√ [ 3961.7^2 - 3959^2 ] ≈ 146.2 mi

CPhill
Apr 12, 2018