Question

A ladder leaning against a wall makes a 60 degree angle with the ground. The base of the ladder is 4 m from
the building. How high above the ground is the top of the ladder?

Answer 1

This is the picture we are working with correct?

Answer 2

@hottiewithabody

Answer 3

What trigonometric function involves a side opposite to the angle and adjacent to the angle?

Answer 4

You there?

Answer 5

They never gave me a picture,

Answer 6

Have you heard the term SOH CAH TOA ?

Answer 7

no

Answer 8

SOH CAH TOA (pronounced SO cuh toe-uh)
is an acronym to help with remembering the trigonometric functions

SOH is sin=opposite/hypotenuse
CAH is cos=adjacent/hypotenuse
TOA is tan=opposite/adjacent

Answer 9

So for this problem, we have an angle, with a known side opposite and adjacent to it. What trigonometric function would we use?

Answer 10

TOA?

Answer 11

Correct, we would use tangent

In the instance of this problem we would have,
\[\tan(60)=\frac{x}{4}\]

Answer 12

The tangent of the angle , 60degrees, is equal to the side opposite of the angle, x, divided by the side adjacent to the angle, 4.

Answer 13

You follow?

So then we would solve for x in this particular instance.
\[x = \tan(60) \times 4\]

Answer 14

http://www.themathlab.com/writings/short%20stories/sohcahtoa/overview.htm

Answer 15

The answer is 6.92820323, round it to where you need it.

Answer 16

ok so your saying x= 240

Answer 17

No, x = 6.92820323

Answer 18

The height that it goes up the wall is 6.92820323 meters up the wall.

Answer 19

x= tan (60) x 4 <----- Im not following you there.

Answer 20

on your calculator, there should be a tangent button (TAN).
You press it and you should see tan(
you type in 60, close out the parenthesis. Then multiply by 4.

Answer 21

for this problem I used the Pythagorean Theorem and got x= 6.63

Answer 22

How did you use the Pythagorean theorem?
I have to go, hopefully @terenzreignz can take over.

Answer 23

I'm here... where were you guys (in this question) ?

Answer 24

Well, I told him/her about soh cah toa.
Explained it in terms of the problem.
Set up the problem.
Told him/her how to plug it into the calculator.

I can't finish because I have to go take a physics final. Wish me luck.

Answer 25

Good luck :)
@hottiewithabody let's get to it...

Answer 26

So you know that we're to use the function "tangent" with this problem, right?

Answer 27

TOA
\[\huge \text{tangent}=\frac{\text{opposite}}{\text{adjacent}}\]

Answer 28

THIS side, with length x, happens to be the side OPPOSITE the angle measuring 60 degrees.

Answer 29

While THIS side, measuring 4, is the side that is ADJACENT to the angle measuring 60 degrees.

If "adjacent" is hard to grasp, it's the side that is NOT the hypotenuse (longest side) and NOT opposite the angle.

Answer 30

So... with that worked out, we find that
\[\huge \tan(60^o) = \frac{x}{4}\]

Answer 31

Multiplying both sides by 4 would yield
\[\huge x = 4\tan(60^o)\]

Answer 32

Now, because I'm a bit particular with precision, let's use this equivalence
(which you may or not have memorised in school, either way...)
\[\huge \tan(60^o)= \sqrt3\]
So it boils down to
\[\huge x = 4\sqrt3\]