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

@gottennis121 @Jaynator495 @Englishguy @SamsungFanBoy

Answer 2

The measures of the angles of a triangle add up to 180 degrees, not 360.
In addition, that deals only angle measurements, not side lengths.

Answer 3

@Keigh2015 Are you studying trigonometry?

Answer 4

It's geometry

Answer 5

Have you learned sine, cosine, and tangent of right triangles?

Answer 6

Yes @mathstudent55

Answer 7

Ok.
We need to use one of those functions.

Answer 8

Would we use cosine?

Answer 9

The figure above shows what we have.
We know distance y and angle x.
I added d, the distance between the moon and the sun, because that is what we want to find.

Answer 10

Look at the figure.
We need d.
In the triangle, d is opposite the right angle.
Is d a leg of the triangle or the hypotenuse of the triangle?

Answer 11

I thing d is the leg of the triangle.

Answer 12

In a right triangle, the legs are the sides that form the right angle.
The hypotenuse is opposite the right angle.

Answer 13

No. d is opposite the right angle, so d is the hypotenuse.
We need to find the length of the hypotenuse.
We have y, the length of a leg.