Question

A shooting star forms a right triangle with the Earth and the Sun, 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 Earth and the shooting star.

Answer 1

Do you know about SOHCAHTOA? Sine, cosine, tangent?

Answer 2

Idk what SOHCAHTOA is but i know what Sine Cosine and Tangent are

Answer 3

Oh ok SOHCAHTOA is just the acronym.
So would you use sine, cosine, or tangent for this problem?

Answer 4

ok hold on let me look at it and i will tell you

Answer 5

Ok is Sine right?

Answer 6

SOHCAHTOA
Sine (of an angle) = Opposite/Hypotenuse
Cosine (of an angle) = Adjacent/Hypotenuse
Tangent (of an angle)= Opposite/Adjacent

Answer 7

So they give you angle X and side y. Side y is adjacent to angle X.
So you have an adjacent side and you need to find length BA which is opposite of angle X.

Answer 8

Do you understand the difference between adjacent and opposite?

Answer 9

Yes Adjacent is at Bc and opposite is at Ba right?

Answer 10

Yes

Answer 11

So which trigonmetric ratio would you use: sine, cosine, or tangent?

Answer 12

Tangent

Answer 13

Correct.
So tan(x) = BA / y

Answer 14

Then to get BA you would rearrange.
y*tan(x) = BA

Answer 15

Ok

Answer 16

Get it now? Any more questions?

Answer 17

@anthonyym sorry my mother called me. so my answer is y*tan(x) = BA?

Answer 18

@anthonyym?

Answer 19

@dayakar is this my answer? y*tan(x) = BA?

Answer 20

@anthonyym do i have my answer right?

Answer 21

Yes, BA, the distance between the Earth and the shooting star, eqauls y*tan(x)