Question

Look at the ramp PQ.



Find the height of the ramp, PR, in meters. (1 point)
2500 sec 23˚
2500 csc 23˚

Answer 1

^those are the other two answers

Answer 2

@AccessDenied Do you mind looking at this quickly?

Answer 3

Sorry, back. :D
I'm not an advocate of using the inverse functions here, but here's how I'd consider it anyways lol

We can assume that the ramp is a right triangle, or else our answer choices are a little odd.
So, we are focusing on angle 23. We know the hypotenuse, and we want to find the opposite side.
Well, the function dealing with these two sides is sine, or in our situation its reciprocal cosecant.
\( \csc \angle A = \large \frac{hyp}{opp} \)

Answer 4

So you would use the cosecant of angle 23 and that would rule out the first and third choices.

Answer 5

Yes.
We then set up an equation:
\(\csc 23^\circ = \frac{2500}{h} \)
Just calling the height "h" here.

If we solve for h, we would have the expression for the height.

Answer 6

Do you need the height though? Because I think it would be 108.7

Answer 7

The question asks for us to find the height of the ramp, which is an unknown in the triangle... so that's essentially what we're finding with the "h".
By solving for h in the equation, we get the expression of the height that's in the answer choices.

Answer 8

So, if we solve for h...
We multiply both sides by "h", which is allowed because the h cannot be 0 anyways.
h csc(23) = 2500

Then divide off the csc(23)
h = 2500/csc(23)

Which we can find in our answer choices. :)

Answer 9

Oh, okay! That makes much more sense now. Thanks so much!

Answer 10

You're welcome! :)