Question

The circle at the right represents Earth. The
radius of Earth is about 6400 km. Find the distance d to the horizon that a person can see on a clear day from each of the following heights h above Earth. Round your answer to the nearest tenth of a kilometer.

Answer 1

supposing that h=9.5 km, the hypotenuse of the triangle shown would be (6400+9.5) km.
The longer leg is simply the radius of the earth: 6400 km. We want to find d.

Use the Pythagorean Theorem.

Answer 2

@mathmale it is just 5 not 9.5 the 9. was the problem number

Answer 3

Ooops. But have you enough info now to solve this problem? If not, please ask questions.

Answer 4

what do i do with the r part of the diagram

Answer 5

that black triangle is a right triangle, isn't it? Your task is to determine the value of d.
Please type out the Pythagorean Theorem and explain it in words to the best of your ability.

Answer 6

a^2+b^2=c^2 thats about how far i am in understanding this problem

Answer 7

side labeled d is a leg and side labeled r is a leg

Answer 8

c would be the longest leg in your right triangle. In this case r=6400 km and h=5km, so the hypotenuse of this right triangle is 6405 km. Agreed or disagreed?

Answer 9

ooh ok agree

Answer 10

6400^2+b^2=6405^2

like that?

Answer 11

Don't you people think we need application of derivative to solve this problem ??

Answer 12

if i knew what that was i could answer you

Answer 13

In that case; simply use a calculator to solve the Pythagoras.. I can't see how to solve it by hand..

Answer 14

highschoolmom: 6400^2+b^2=6405^2 is correct. All you need to do is to solve for b.
Know what to do to accomlish that? If not, I'd be glad to guide you thrugh the process.

Answer 15

4096000+b^2=41024025

those numbers look really large....

Answer 16

Don't worry about that. Looks like you're on the right track.

Answer 17

Mom: How are you doing?

Answer 18

b^2=64025

Answer 19

sqrt b^2=sqrt 64025
b=253.03

Answer 20

i think that is right

Answer 21

Cool. Make that 253 km and you'll be right on target. See you again soon.

Answer 22

thanks :)

Answer 23

Good going!