Question

If a ramp is 12'' high and rises at an angle of 17'' how is the base, rounded to the nearest inch, 39.25?

Answer 1

Is it 17 degrees?

Answer 2

On a triangle, so yes I think. and
I was reading a conversation on here from one month ago that had my same question. They got the answer "39.25". I tried to do it myself, to see if I could get the answer, but I cannot get the same answer.

Answer 3

So for this, what trigonometric function did you use?

Answer 4

Tangent?

Answer 5

Correct, and tangent=opposite/adjacent right?

Answer 6

Yes so tan17=12/x

Answer 7

And then, I guess I don't do it the same way they did. I don't seem to know how to go further.

Answer 8

Try swapping tan(17) and x. So that x=12/(tan(17))

Answer 9

And now what?

Answer 10

What should I input into my calculator?

Answer 11

I'm trying different things. I still don't know what to do to this thing we set up though. Do I cross multiply/divide or something? 17x=12?

Answer 12

What I typed into my calculator was 12/tan(17)=39.250023142

Answer 13

I didn't try anything like that. When I typed THAT in just now, the outcome was: 41.92698775. Is there a certain mode or something it needs to be in?

Answer 14

\[\tan(17)=\frac{12}{x}\]
You then swap the x and tan(17)
\[x=\frac{12}{\tan(17)}\]

And, make sure that your calculator is in degree mode, if I had to bet, you are still in radian mode.

Answer 15

What calculator do you use?
TI-83 or TI-84? Something else?

Answer 16

Oookay, I finally got "39.25" ......

Answer 17

TI-83 plus

Answer 18

Yeah, so for that calculator you press "mode" and it should be the third line down to change the radian vs. degree mode.
But good job on getting the correct answer.
If you have another question, close this one and feel free to ask!

Answer 19

Thanks a lot for your help. but Now that I got the same answer that they did, 39.25 (rounded), I must ask why we had to change the 17 and x?

Answer 20

Like, what would tell the person to think "we must change those two's locations"?

Answer 21

It was a trick that I was taught when I learned geometry and trigonometry.
Also, if you use basic algebra the answer that you get is clearly not correct.

Answer 22

Riight. Well, I'm just trying to study for a test tomorrow. Will that trick help me on those kinds of problems on my upcoming test?

Answer 23

For this one, how would you solve for x?

Answer 24

Um... divide it by those other numbers.

Answer 25

For this one, you would have to do basic algebra, and x should equal 11.48.
If worse comes to worse, try it algebraically and then try it with the swap method that I showed you. It doesn't apply in all situations, but if you do both, it is pretty obvious which is the right answer. For example, which one is most reasonable for the question I posed you.
x=11.48 or x=0.08

Answer 26

x=11.48 I think

Answer 27

It is a multiple choice test, so if I do those two methods, I can probably ground the possible choices down to one good one and pick it.

Answer 28

Using what you've helped me with.

Answer 29

Exactly, you have to think about it in terms of what is a feasible answer.
For this, what would be the answer?

For multiple choice, it helps alot.

Answer 30

If you are having problems, try solving for x and then y.

Answer 31

What is 15 to the x there? I don't know if it is adjacent/opposite or what?

Answer 32

You have to think about the adjacent and opposite in terms of the angle. For this particular problem the 15 is opposite of the angle of 39, x is adjacent, and y is the hypotenuse.

Have you learned SOH CAH TOA?

Answer 33

Yes

Answer 34

Ok, so for the problem I proposed to you. What is the tangent of 39? and what is the cosine of 39?

Answer 35

Or sine of 39?

Answer 36

39tan=15/x

Answer 37

39sin=15/x ?

Answer 38

Ok, so
tan(39)=15/x
cos(39)=x/y
sin(39)=15/y
Can you go from there?

Answer 39

NO the sine of 39 is 15/y

Answer 40

Yeah

Answer 41

Good. Now you just have to solve for the variables.

Answer 42

Solve for each of the trig function things?

Answer 43

The variables are x and y. Which means that you have to do the swap for the tangent part. And the other part, you would do the same.

Answer 44

so tan of x=15/39 because of the swap method.

Answer 45

I'm going through my notes to see what I do next...

Answer 46

so tan of x=15/39 because of the swap method.

x=15/tan(39), dont forget that it is the tan(39), not just 39

Answer 47

Ohhh I didn't move the Tangent WITH the 39

Answer 48

18.52345735

Answer 49

Do I have to do that for all of them? So now I only currently have one answer? Which would be the answer for the tangent...

Answer 50

Correct, and you always move the trig function.

Answer 51

I will try to get the others now...

Answer 52

I think the SIN is 23.8 but what do I do with the COS since I am not supplied with any real numbers?

Answer 53

You already solved for the x, so you have that value. The answer should be the same as the sin one. AND for future reference, the sin one would be the best answer for this particular problem.

Answer 54

I only need to work one of either SIN or COSIN?

Answer 55

Until I have a number for one of the values for a variable?

Answer 56

Correct, they would be the same answer for the length of the hypotenuse. The sin answer would be the most accurate because you are using a given value in the calculation of the answer rather than a rounded number that you found.
There is only one way to find x, and two ways to find y.

Answer 57

I did them both and they're both 23.8 so I know did this right so far.

Answer 58

I took physical notes on everything we went over, so I think I can study them, do some more of these problems from my school textbook, and I should be fine on this.

Answer 59

That is good! If you need more help, feel free to post another question.

Answer 60

Thanks a lot, Austin. I'll delete this now

Answer 61

Goodbye.

Answer 62

You dont need to delete, just close. And you are very welcome.