## anonymous one year ago 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.

1. anonymous

2. campbell_st

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

3. anonymous

thanks

4. anonymous

but i need it to be more detailed

5. anonymous

@jdoe0001 can you help me

6. campbell_st

so what detail do you need...?

7. anonymous

8. campbell_st

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

9. anonymous

okay

10. anonymous

then..?

11. campbell_st

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

12. anonymous

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

13. anonymous

?

14. campbell_st

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

15. anonymous

sine

16. campbell_st

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

17. anonymous

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

18. campbell_st

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..?

19. anonymous

tangent

20. anonymous

21. campbell_st

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

22. anonymous

what do you mean by the subject of the equation?

23. campbell_st

well ES is in the denominator of the fraction you need to rewrite the equation with ES = something

24. anonymous

sorry but im confused

25. campbell_st

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

26. anonymous

okay thanks is that all?