Question

A ladder leaning against a wall makes an angle of 45º with the ground. If the length of the ladder is 20 feet, find the approximate distance of the foot of the ladder from the wall

Answer 1

I used Pythagoras's theorem knowing that both sides of a right triangle with 45° angles have 2 equal sides and then the hypotenuse. I got 10(square root)2

Answer 2

Using Cosine ratio:

`\cos \theta = \frac{\text{Adjacent side}}{\text{hypotenuse side}}`

As per the statement:

A ladder leaning against a wall makes an angle of 45º with the ground.

⇒Angle of elevation
`\theta = 45^(\circ)`

It is also given that the length of the ladder is 20 feet.

Length of ladder = 20 feet.

We have to find the approximate distance of the foot of the ladder from the wall.

Let y be the distance of the foot of the ladder from the wall.

You can see the diagram as shown below in the attachment:

Hypotenuse side = Length of ladder = 20 feet

Adjacent side = Distance of foot of the ladder from the wall = y feet

Using cosine ratio we have;

Substitute the given values we have;

`\cos 45^(\circ) = (y)/(20)`

Multiply both sides by 20 we have;

⇒
`20 \cdot \cos 45^(\circ) = y`

Simplify:

`14.1421356 = y`

or

y = 14.1421356 feet

Therefore, the approximate distance of the foot of the ladder from the wall is, 14.14 feet