Question

A shooting star forms a right triangle with the Earth and the Sun, as shown below:

A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x degrees and the side between the Earth and the Shooting Star is labeled y.

A scientist measures the angle x and the distance y between the Earth and the shooting star. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun.

Answer 1

you have a right triangle so you can find the distance using a trig ratio...

y represents the opposite side

the distance between earth and the sun would be the adjacent side...

so which ratio..?

hope it helps

Answer 2

thanks

Answer 3

but i need it to be more detailed

Answer 4

@jdoe0001
can you help me

Answer 5

so what detail do you need...?

Answer 6

what was the last question you asked about?

Answer 7

so in this right triangle question... you need to identify the trig ratio that uses opposite and adjacent sides...

Answer 8

okay

Answer 9

then..?

Answer 10

well that's for you to answer... its a fundamental for success in trigonometry to know the 3 basic ratios... and what sides they need...

some people use SOHCAHTOA to help remind them

Answer 11

yes i know it that :) i use it too so i need to identify which one to use

Answer 12

?

Answer 13

so which of the 3 trig ratios uses the opposite and adjacent side...?

Answer 14

sine

Answer 15

nope... use the mnemonic... sine = opp/hyp SOH

Answer 16

okay so we can say that in this we use the SOH to identify the distance between sun and earth?

Answer 17

no.... you don't have a measurement on the hypotenuse... so you can't use any ratio that uses the hypotenuse

sin= opp/hyp and cos = adj/hyp

so which ratio is left..?

Answer 18

tangent

Answer 19

tangent= opposite/adjacent

Answer 20

great so label the distance from earth to the sun ES

then using the tan ratio you can say

\[\tan(x) = \frac{y}{ES}\]

then make ES the subject of the equation.

hope it helps

Answer 21

what do you mean by the subject of the equation?

Answer 22

well ES is in the denominator of the fraction

you need to rewrite the equation with

ES = something

Answer 23

sorry but im confused

Answer 24

ok... your goal is to find the distance from the Earth to the Sun

when you write the tan ratio you get

\[\tan(x) = \frac{y}{ES}\]

you need to manipulate the equation, so that its in the form

ES = something that uses tan(x) and y

Answer 25

okay thanks is that all?