Question

PLEASE HELP!!

A 12 ft ladder leans against the side of a house. The top of the ladder is 10 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.

Answer 1

The angle of elevation x of a 12 ft ladder reaching 10 ft high on a wall can be found using the cosine function. It is approximately 33.6 degrees.

Step-by-step explanation:

To solve for x, the angle of elevation of a ladder leaning against a wall, we can use trigonometric ratios. Since we know the length of the ladder (12 ft) and the height it reaches on the wall (10 ft), we can use the cosine function. The cosine of an angle in a right triangle is the adjacent side over the hypotenuse, so:

cos(x) = adjacent side / hypotenuse

cos(x) = 10 ft / 12 ft

To find the angle x, we take the arccosine (inverse cosine) of the ratio.

x = arccos(10 ft / 12 ft)

Using a calculator, x ≈ arccos(0.8333)

x ≈ 33.6 degrees

So, the angle of elevation of the ladder is approximately 33.6 degrees.

Answer 2

`x=56.4\degree` to the nearest tenth.

Step-by-step explanation:

Recall the mnemonics SOH.

This means that;

`\sin(x)=(Opposite)/(Hypotenuse)`

From the diagram, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.

We substitute the values to get;

`\sin(x)=(10)/(12)`

`\sin(x)=(5)/(6)`

Take the sine inverse of both sides

`x=\sin^(-1)((5)/(6))`

`x=56.4427\degree`

`x=56.4\degree` to the nearest tenth.