Question

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.
The angle made by the ladder with the ground is______
degrees, and the length of the ladder is ________
inches.

Answer 1

do you know the angle measure

Answer 2

So as the problem states, the ladder touches the wall at 50 inches from the ground and the length from the base of the wall to the base of the ladder is 30 inches as depicted by the diagram below:

Answer 3

@mmarcum19 my question to you is, do you know the formula to use to find the length of the ladder?

Answer 4

like the Pythagorean theorem but, that only gives me a side . I don't know how to find angles

Answer 5

Sure, we will get to angles next, but let's find the length of the ladder first.

We'll let
a represent the height from the floor to where the ladder touches the wall, and
b represent the distance from the base of the wall to the base of the ladder and
c represent the length of the ladder.

Using Pythagorean Theorem, what would be the length of the ladder?

Answer 6

\[50^2 +30^2=C^2
2500+900=c^2
3400=c^2

Answer 7

@mmarcum19 I see that you have found \(c^2\). Great job, but we still need to find the value of \(c\). Do you know how to find \(c\) now that you've found \(c^2\)?

Answer 8

no

Answer 9

To find \(c\), root both sides as follows:

\(c^2 = 3400\)
\(c = \sqrt{3400}\)

Input \(\sqrt{3400}\) into your calculator to find the value of \(c\)

Answer 10

58.3?

Answer 11

Correct. So now that we have found that, we must use trig ratios to find the angle made by the ladder with the ground:

Answer 12

I don't know trig ratios

Answer 13

For simplicity, let's just say:
the side length of the ground is 30 in.
the side length of the wall is 50 in.
the side length of the ladder is 58.3 in.

So in terms of angle x, the ground side is the adjacent side, the wall side is the opposite side and the ladder side is the hypotenuse side.

Answer 14

Okay

Answer 15

The simplest way to start explaining trig ratios is to start with SOH CAH TOA. You may have heard of that before.

SOH represents that \(\sin(x) = \dfrac{\text{opposite}}{\text{hypotenuse}}\)
CAH represents that \(\cos(x) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\)
TOA represents that \(\tan(x) = \dfrac{\text{opposite}}{\text{adjacent}}\)