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 sun and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the moon.

Answer 1

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 sun and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the moon.

Answer 2

Man I hate things like this.

Answer 3

@Ledah yeah me to /: I suck at Geometry.

Answer 4

Okay so we know it's a trig thingy

here are the operations:
Sin = opposite ÷ hypotenuse
Cos = adjacent ÷ hypotenuse
Tan= opposite ÷ adjacent

Answer 5

Yeah, I know it's going to have to involve something like that I just don't get how to answer the question or what to answer.

Answer 6

We "know" the hypotenuse so we need to find the adjacent and opposite c;

Answer 7

Okay, so now how do I find them?

Answer 8

@smoothmath would we do the opposite divided by the hypotenuse on this one?

Answer 9

I know it's going to involve something like Y cos x, but I'm not so sure thats anywhere near right,

Answer 10

Well I tagged one of my besttiee friends so he should be able to come help. He's really good at these.

Answer 11

Okay, Thanks a bunch!(:

Answer 12

No problem :D

Answer 13

Hey, sorry I didn't notice you tagged me. Both of you, pay attention.
The whole approach is to use the definition of one of those trig functions to set up an equation. That's the slightly tricky part, but once we've set up the equation, it's easy to solve it.

Answer 14

*listening*

Answer 15

So first, decide which trig function to use. To do this, we look at which side we know and which side we want to know, and we decide which two those are out of; hypotenuse, adjacent, opposite.

So, for this one, look at the side you know, decide which side you want to know, and tell me which sides those are. Becca, I know you know how to do this. Let Math_Is_Confusing tell me =)

Answer 16

Hpmh, he left :'c

Answer 17

Okay so the side you want to know would be the oppostie side, or moon to earth?

Answer 18

We want to know all three, but we're going to solve for the two we want to know just one at a time. So pick one you want to know, and we'll solve for it.
Moon to earth is a good choice, and you are correct. It is OPPOSITE from the angle we know.
And what is the side we already know?

Answer 19

The hypotenuse, or moon to sun

Answer 20

Very good. So we want to set up an equation involving Hypotenuse and Opposite. Which trig function uses those two things?

Answer 21

Sin, opposite over hypotenuse

Answer 22

Very good. So this is the hardest part, but I'm confident you can do it. You chose Sin, now write an equation using the definition of sin.
Sin(the angle) = opposite / hypotenuse

Answer 23

Sin x= opposite over y?

Answer 24

Yeah, very good. In a normal problem, we would have numbers for x and y, so we would then have an equation we could solve.

Answer 25

Understand? Don't let sin intimidate you. You just punch it into your calculator with the correct angle, make sure you're in radians or degrees, depending on how your angle is measured, then hit enter.

Answer 26

Thanks so much! I understand it now! I'm taking Geometry online, so the way they explained how to do it was weird, but i get it now. (:

Answer 27

Yeah, so just the quick review of what we do:
1) Decide which two sides we're going to look at, one side we know and one side we want to know.
2) Figure out which two sides those are out of opposite, adjacent, and hypotenuse, and that tells us which trig function to use.
3) Use the definition of the trig function, plug in the angle and the sides to set up an equation.
4) Solve the equation. Easy peasy parchesie.

Answer 28

Remember now, @rebeccaskell94 ?

Answer 29

Thanks so much again!

Answer 30

My pleasure, buddy! =D

Answer 31

Yes, dollface.