Question

The moon forms a right triangle with the Earth and the sun during one of its phases, as shown below.
A scientist measures the angle x and the distance y between the Earth and the sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the sun.

Answer 1

plz help!

Answer 2

The scientist has to be a Mathematician too. Trig.

Answer 3

yeah, but how? What ratio?

Answer 4

sin, cos, tan? I dont get it

Answer 5

Well. We have the adjacent and the hypotenuse to be acted upon in this particular case.

Answer 6

okay....

Answer 7

Do you recall a ratio which has both adjacent and hypotenuse?

Answer 8

cos?

Answer 9

sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent

Answer 10

so it's cos?

Answer 11

That's right. You may now start with\[\cos x = {y \over d} \]Where d is the distance between sun and moon.

Answer 12

Yes, it is cos.

Answer 13

yes

Answer 14

ok

Answer 15

then what?

Answer 16

That's it. We don't know what \(y\) is, but that scientist does.

Answer 17

so it's just cos x = y/d?

Answer 18

We may have continued if we knew \(y\), but now here.

Answer 19

we can only use x and y to find the adjacent side, so we can't use the hypotenuse which is unknown

Answer 20

Where \(d\) is the distance needed to be calculated.

Answer 21

okay, thanks! I wasn't sure exactly how to solve without using the actual numerical values haha

Answer 22

You use a calculator for that.

Answer 23

We could've done the thing if we knew what x,y were.