Question

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

Answer 1

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.
Can someone please help me out with this question? :)

Answer 2

@ganeshie8

Answer 3

@hartnn

Answer 4

@Luigi0210

Answer 5

@radar

Answer 6

Hey @shinebrightlikeadimon do you still need help??

Answer 7

my sister and i share this account she posted this question so let me go ask her really quick

Answer 8

yes i do

Answer 9

Okay dokay

Answer 10

@dmezzullo

Answer 11

thank you :)

Answer 12

Um, I was looking at the question. I am not totally sure how to do it but if my memory is correct you need to multiply the x and y. Then some more. Sorry, I don't really know how to help. I am better in biology.

Answer 13

oh okay can you help me? @hartnn

Answer 14

we = scientist
so we want distance BC
and we have AB = y ,
angle C = x

Answer 15

see the angle 'x'
AB is what of 'x' ??
BC is what of 'x' ??
your options are : opposite side, adjacent side, hypotenuse

Answer 16

so you want me to tell u what is x?

Answer 17

i want you to tell whether AB is opposite side to x ?? or adjacent side to x ? or is AB the hypotenuse ?

Answer 18

opposite side?

Answer 19

thats correct
what about BC ?

Answer 20

adjacent side

Answer 21

right ,

so do you know which trigonometric ratio relates opposite side and adjacent side ?

Answer 22

TOA?

Answer 23

correct!
so tan is the ratio you will use here

Answer 24

what will tan x = ... ?

Answer 25

opposite/adjacent?

Answer 26

in your triangle, ABC
tan x = ... ?

Answer 27

y/AB which can be d.. so y/d?

Answer 28

correct!
so in

tan x = y/d

only 'd' is unknown!

Answer 29

and you can find it using

d = y/ tan x

Answer 30

oh okayy!

Answer 31

so, can you please help me out on explaining this in complete sentences?

Answer 32

you got the method, try to describe it in your own words, if there is any error, i will help you correct it :)

Answer 33

okay :) so we're trying to find the distance between Earth and Sun which is line segment BC and to do that we have to use the trigonametric ratio TOA ( Tangent Opposite Adjacent) which in this case will be tan(x) = y/d ; and when you get d by itself which is the distance between Eart and the Sun . So, d = y/tanx (x)?

Answer 34

yes, that should work, you can add some details,
like in triangle ABC
opposite side to x angle is AB which = y
and adjacent side to angle x is BC which = d
and then say that tan x = AB/BC = y/d

Answer 35

okay thank you so much for your help!! :) @hartnn

Answer 36

welcome ^_^