Question

HI PLEASE SOMEONE HELP ME WITH SOME QUESTIONS FOR GEOMETRY

Answer 1

@poopsiedoodle Can you please help me?

Answer 2

@hero

Answer 3

Here's a suggestion.
Post one of the questions, and maybe someone will help you.

Answer 4

can you help me with a couple please?

Answer 5

Once again, post a question.

Answer 6

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 7

Do you have the figure?

Answer 8

sorry, i was taking the screenshot of it

Answer 9

No problem.
I assume you are learning trigonometry of right triangles.

Answer 10

yes. its one of the chapters in my online geometry course

Answer 11

Ok.
Here we go.

Answer 12

okay. thank you so much. I really appreciate this

Answer 13

In your figure, you see you have a right triangle with right angle B.
The hypotenuse is AC, and that is the distance you want to find.
Also, you know angle x, and you know y.

Answer 14

In this triangle, the hypotenuse is AC. We already know that. We want to find this length.
There are 2 legs in a right triangle.
In our right triangle the legs are BC with known length y, and AB, whose length we don't know but are also not interested in.

Answer 15

thats correct. we only need BC

Answer 16

In a right triangle, to distinguish between the two legs, we call them the adjacent leg and the opposite leg. These terms for the legs are with reference to an acute angle of the right triangle. The angle we are using is angle C since we know its measure is x.

Answer 17

so would be using SOH CAH TOA?

Answer 18

Exactly.
For angle C, is BC adjacent or opposite?

Answer 19

I would say adjacent

Answer 20

Correct.
We are only interested in three things in this triangle.
Known angle C (measuring x)
Known adjacent leg BC (measuring y)
Unknown hypotenuse AC

Answer 21

Using SOH CAH TOA, which one of the trig functions sine, cosine, tangent, relates the adjacent leg to the hypotenuse?

Answer 22

Cosine??

Answer 23

Correct.
CAH : cos A = adj/hyp

Answer 24

We can write an equation using the cosine equation and our known and unknown info.

\(\cos \theta = \dfrac{adj}{hyp} \)

\(\cos C = \dfrac{BC}{AC} \)

\(\cos x = \dfrac{y}{AC} \)

Since x is known, cos x is also known. y is known, so the only unknown is AC, which can be solved for.

\(AC = \dfrac{y}{\cos x} \)

Answer 25

so how would i put this in a essay form? this is what i have so far: To measure the distance between the the Earth and the shooting star, the scientist would be using SOH CAH TOA. For this particular question, they would be using CAH or cosine. cos A = adjacent/hypotenuse.

Answer 26

Very good so far.

Answer 27

Wait. I read the problem wrong.

Answer 28

I'm really sorry, but let's look at it again.

Answer 29

So should i write about the equations?
like these: cosθ=adj/hyp

cosC=BC/AC

cosx=y/AC

Answer 30

so we need to completely restart??

Answer 31

The distance the problem is asking for is the distance between the shooting start and the Earth. We need to find AB, not AC.

Answer 32

It's still a SOH CAH TOA problem only a different one.

Answer 33

would they still be using cosine or would they go to tnagent?

Answer 34

tagent*

Answer 35

Wow, I see that you're smart.
We will be using the tangent.
We have x, the angle measure, and we have y, the adjacent side.
The unknown is AB. AB is the opposite leg.
The function that relates the opposite and adjacent legs is the tangent.

TOA: tan A = opp/adj

Answer 36

\(\tan x = \dfrac{opp}{adj} \)

\(\tan x = \dfrac{AB}{y} \)

Answer 37

lol i try. but when i do it alone, i usually dont do too well.. so im just trying to finish out the course right now. at 12am. on my bedroom floor

Answer 38

Now we solve for AB, the distance between the shooting star and the Earth.

Answer 39

\(AB = y \tan x\)

Answer 40

Since I started you off incorrectly, I did the following to make it up to you. I fixed your beginning of the answer.

To calculate the distance between the the Earth and the shooting star, the scientist would be using SOH CAH TOA. For this particular question, he would be using TOA or tangent. tan A = opposite/adjacent.

Answer 41

thank you

Answer 42

Now you need to finish it.

Answer 43

so here is what i have now, after correcting it:
To measure the distance between the the Earth and the shooting star, the scientist would be using SOH CAH TOA. For this particular question, they would be using TOA or tangent.
The equation would be opposite/adjacent
so y/AB
Now, you would solve for AB
AB=y tan x

Answer 44

You have to be careful with which side is opposite and which side is adjacent.

Answer 45

so would the adjacent be C?

Answer 46

To calculate the distance between the the Earth and the shooting star, the scientist would be using SOH CAH TOA. For this particular question, they would be using TOA or tangent.
The equation would be opposite/adjacent
so tan x = AB/y
Now, you would solve for AB
AB=y tan x

Answer 47

Also, change "measure" to "calculate"
The scientist is calculating the distance based on some measurements. He is not measuring the distance.

Answer 48

alright. i changed it

Answer 49

Great, you got it!

Answer 50

so is that all? is that everything i was supposed to write?

Answer 51

@mathstudent55

Answer 52

Yes. It looks good to me. You've explained how to calculate the distance from the shooting start to Earth.