sebastiangonzagonza
  • sebastiangonzagonza
HI PLEASE SOMEONE HELP ME WITH SOME QUESTIONS FOR GEOMETRY
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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sebastiangonzagonza
  • sebastiangonzagonza
@poopsiedoodle Can you please help me?
sebastiangonzagonza
  • sebastiangonzagonza
@hero
mathstudent55
  • mathstudent55
Here's a suggestion. Post one of the questions, and maybe someone will help you.

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More answers

sebastiangonzagonza
  • sebastiangonzagonza
can you help me with a couple please?
mathstudent55
  • mathstudent55
Once again, post a question.
sebastiangonzagonza
  • sebastiangonzagonza
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.
mathstudent55
  • mathstudent55
Do you have the figure?
sebastiangonzagonza
  • sebastiangonzagonza
sebastiangonzagonza
  • sebastiangonzagonza
sorry, i was taking the screenshot of it
mathstudent55
  • mathstudent55
No problem. I assume you are learning trigonometry of right triangles.
sebastiangonzagonza
  • sebastiangonzagonza
yes. its one of the chapters in my online geometry course
mathstudent55
  • mathstudent55
Ok. Here we go.
sebastiangonzagonza
  • sebastiangonzagonza
okay. thank you so much. I really appreciate this
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
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.
sebastiangonzagonza
  • sebastiangonzagonza
thats correct. we only need BC
mathstudent55
  • mathstudent55
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.
sebastiangonzagonza
  • sebastiangonzagonza
so would be using SOH CAH TOA?
mathstudent55
  • mathstudent55
Exactly. For angle C, is BC adjacent or opposite?
sebastiangonzagonza
  • sebastiangonzagonza
I would say adjacent
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
Using SOH CAH TOA, which one of the trig functions sine, cosine, tangent, relates the adjacent leg to the hypotenuse?
sebastiangonzagonza
  • sebastiangonzagonza
Cosine??
mathstudent55
  • mathstudent55
Correct. CAH : cos A = adj/hyp
mathstudent55
  • mathstudent55
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. \(AC = \dfrac{y}{\cos x} \)
sebastiangonzagonza
  • sebastiangonzagonza
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.
mathstudent55
  • mathstudent55
Very good so far.
mathstudent55
  • mathstudent55
Wait. I read the problem wrong.
mathstudent55
  • mathstudent55
I'm really sorry, but let's look at it again.
sebastiangonzagonza
  • sebastiangonzagonza
So should i write about the equations? like these: cosθ=adj/hyp cosC=BC/AC cosx=y/AC
sebastiangonzagonza
  • sebastiangonzagonza
so we need to completely restart??
mathstudent55
  • mathstudent55
The distance the problem is asking for is the distance between the shooting start and the Earth. We need to find AB, not AC.
mathstudent55
  • mathstudent55
It's still a SOH CAH TOA problem only a different one.
sebastiangonzagonza
  • sebastiangonzagonza
would they still be using cosine or would they go to tnagent?
sebastiangonzagonza
  • sebastiangonzagonza
tagent*
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
\(\tan x = \dfrac{opp}{adj} \) \(\tan x = \dfrac{AB}{y} \)
sebastiangonzagonza
  • sebastiangonzagonza
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
mathstudent55
  • mathstudent55
Now we solve for AB, the distance between the shooting star and the Earth.
mathstudent55
  • mathstudent55
\(AB = y \tan x\)
mathstudent55
  • mathstudent55
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.
sebastiangonzagonza
  • sebastiangonzagonza
thank you
mathstudent55
  • mathstudent55
Now you need to finish it.
sebastiangonzagonza
  • sebastiangonzagonza
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
mathstudent55
  • mathstudent55
You have to be careful with which side is opposite and which side is adjacent.
sebastiangonzagonza
  • sebastiangonzagonza
so would the adjacent be C?
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
Also, change "measure" to "calculate" The scientist is calculating the distance based on some measurements. He is not measuring the distance.
sebastiangonzagonza
  • sebastiangonzagonza
alright. i changed it
mathstudent55
  • mathstudent55
|dw:1439784419738:dw|
mathstudent55
  • mathstudent55
Great, you got it!
sebastiangonzagonza
  • sebastiangonzagonza
so is that all? is that everything i was supposed to write?
sebastiangonzagonza
  • sebastiangonzagonza
@mathstudent55
mathstudent55
  • mathstudent55
Yes. It looks good to me. You've explained how to calculate the distance from the shooting start to Earth.

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