Question

From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 63°, as shown below. If the distance between the radio antenna and the library is 24 miles, how many miles high is the balloon?

Answer 1

@Luis_Rivera ?

Answer 2

@ganeshie8 ?

Answer 3

You've got a right triangle here. The balloon is at the top, next to the 63° angle, directly below it is a 90° angle, and across town is a (90-63=)27° angle. Use either the 63° or the 27° angle and the 24-mile distance on the ground to get from tangent or cotangent to your height.

Answer 4

So which one do I use? 63 or 27? What formula should I plug it in to

Answer 5

@Numb3r1

Answer 6

It doesn't really matter which angle you use, but because of the way calculators work it is slightly easier to get the tangent of an angle. Have you seen the formulas which relate trigonometric functions to two sides of a right triangle?

Answer 7

Mmm, remind me?

Answer 8

of the formulas

Answer 9

Tangent=opposite/adjacent. Cotangent=adjacent/opposite=1/tangent.

Answer 10

oh yeah, I know those

Answer 11

So you would do 90/27?

Answer 12

orrr what? @Numb3r1

Answer 13

No, you take the tangent of 27 (which equals opposite/adjacent) and multiply by the adjacent distance (24) to find the opposite.

Answer 14

I got a negative -_-

Answer 15

Are you sure you took the tangent of 27°? If your calculator is in radian mode, you need to correct for that.

Answer 16

It was in Radians not degrees, oops

Answer 17

Ii got 12.22

Answer 18

That sounds about right.