Question

the airplane door is 19 feet off the ground and the ramp has a 31 degree angle of evaluation. what is the length y of the ramp?

Answer 1

@AZ

Answer 2

Let's draw the image, okay?

Answer 3

ok

Answer 4

Does that make sense? The ramp is on the ground and at an angle of 31 degrees to reach the door which is 19 feet high

and we want to calculate the length of the ramp

Answer 5

yeah but how

Answer 6

Have you learned about sin cos or tan?

Answer 7

yes but i dont get it

Answer 8

Sure, we can cover it again

Answer 9

Have you ever heard of SOH CAH TOA

Essentially, it's an acronym to help you remember the trigonometric functions

sin of an angle equals the opposite side over the hypotenuse

We write that as
sin \(\theta\) = opposite/hypotenuse

Do you see the initials?
Sin = Opposite/ Hypotenuse

SOH

Similarly, for cosine and tangent

cos \(\theta\) = adjacent/hypotenuse

CAH

tan \(\theta\) = opposite/adjacent

TAH

Answer 10

are you a teacher

Answer 11

Here's an image to help you see it together

Answer 12

ok

Answer 13

No haha, I'm just a student like you :)

Answer 14

cool:)

Answer 15

So in the image I drew, do you see that \(\theta\) is going to be the angle which is 31

We're looking for the length of the ramp which is the hypotenuse
And we know the side opposite of the angle

So would we use sin, cos, or tan?

Answer 16

ok

Answer 17

im sorry but its late can you just tell me the answer and we can go over it tomorrow

Answer 18

I would love to but the purpose of this site is to help teach and learn. If I gave you the answer, I'd be breaking the rules and get in trouble

It'll only take like 3 minutes if you work with me to get to the correct answer!

Answer 19

ok

Answer 20

Remember

sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

we know the side OPPOSITE to the angle
and we want to know the hypotenuse

which one do we use?
which one has both the opposite and the hypotenuse

Answer 21

sin?

Answer 22

Exactly!

So remember how we set it up?

\(\sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}\)

so our angle or \(\theta\) is 31

and the side opposite is 19

do you know how to solve for the hypotenuse?

(You have to use a calculator to find sin 19 by the way)

Answer 23

no how do you put into calculator

Answer 24

You can use Google

but you have to be careful that you're doing sin 31 degrees

otherwise it'll do 31 radians which is not what we want

so https://www.google.com/search?q=sin+31+degrees

Answer 25

So what is sin 31 degrees = ?

Answer 26

0.5150

Answer 27

??

Answer 28

Good! So now we have

\(\sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}\)

\(\sin 31^o = \dfrac{19}{\text{hypotenuse}}\)

\( 0.5150 = \dfrac{19}{\text{hypotenuse}}\)


and think of the hypotenuse like it's an 'x'

\( 0.5150 = \dfrac{19}{x}\)

How would you solve for x?

Answer 29

why do i need t solve for x its just y

Answer 30

oh wait nvm haha

Answer 31

im so dumb

Answer 32

i dont know how to solve for x

Answer 33

haha yeah, we can use any letter but 'x' is the one that's most commonly used in math

Answer 34

so 0.52 is the answer
cause you round it to the tenth place

Answer 35

That's not a problem

\( 0.5150 = \dfrac{19}{x}\)

So we have 'x' in the denominator. What happens if we multiply 'x' on both sides

So essentially, how would you simplify

\( 0.5150 \times x= \dfrac{19}{x} \times x\)

Answer 36

ok so how would you simplify it

Answer 37

true

Answer 38

yeah

Answer 39

So we're left with

0.5150 * x = 19

can you solve for x now?

Answer 40

no how do you put that in a calculator

Answer 41

uhh you wouldn't be able to put it into a normal calculator

but this is something you should be able to do on your own now

Answer 42

im dumb trust me i cant

Answer 43

you want to get 'x' all by itself

right now, it's being multiplied with 0.5150

so to get x all by itself, and essentially move the 0.5150 to the other side, you have to do the opposite of multiplication

what is the opposite of multiplication?

Answer 44

division

Answer 45

Exactly!! So we divide 0.5150 on both sides

So all you need to do is divide 19 by 0.5150

x = 19 / 0.5150

x = ??

Answer 46

36.9

Answer 47

There you go!

Answer 48

thank you so much ill keep in touch

Answer 49

Of course! You're welcome!