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avatar+63 

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.

 

https://static.k12.com/nextgen_media/assets/1576278-IM3_150120_060404.jpg

summertastic1011  Apr 12, 2018
 #1
avatar+545 
+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)

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #2
avatar+63 
+1

nevermind

summertastic1011  Apr 12, 2018
edited by summertastic1011  Apr 12, 2018
 #3
avatar+63 
0

can someone answer another question?

summertastic1011  Apr 12, 2018
 #4
avatar+545 
+1

no problem

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #5
avatar+545 
+1

yes me please

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #6
avatar+63 
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
 #7
avatar+545 
+1

nevermind

 

winkwinkwink

lynx7  Apr 12, 2018
edited by lynx7  Apr 12, 2018
 #8
avatar+63 
0

oh ok lol

summertastic1011  Apr 12, 2018
edited by summertastic1011  Apr 12, 2018
 #9
avatar+545 
+1

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

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #10
avatar+63 
0

im not sure i dont think so 

summertastic1011  Apr 12, 2018
 #11
avatar+545 
+2

the answer is 146.2

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #12
avatar+63 
0

oh ok how did you get the answe?

summertastic1011  Apr 12, 2018
 #13
avatar+545 
+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
avatar+87639 
+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

 

 

cool cool cool

CPhill  Apr 12, 2018
 #15
avatar+63 
+1

thank you both so much!

summertastic1011  Apr 12, 2018
 #16
avatar+545 
+2

no problem any time 

 

 

winkwinkwink

lynx7  Apr 12, 2018
 #17
avatar
0

There is a very simple formula for this kind of problem:

 

D = ~Sqrt[1.5 x H], where D =distance in miles, H=Height in feet.

D =~sqrt[1.5 x 2.7 miles x 5,280 feet]

D =~Sqrt[ 21,384]

D=~ 146.23 miles - distance to the horizon.

Guest Apr 13, 2018

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