Question

A fireman is standing 30 m directly west of a burning building. His ladder reaches 50m up the side of the building. What is the angle of elevation to the closest degree of his ladder?

Answer 1

As per the statement:

You can see the diagram as shown below.

Distance of fireman stands away from the building = 30 m

Length of the ladder = 50 m

Using Cosine ratio:

`\cos \theta = \frac{\text{Adjacent side}}{\text{Hypotenuse side}}` ....[1]

From the diagram:

Adjacent side = 30 m

Hypotenuse side = 50 m

Substitute these values in [1] to solve for angle of elevation(
`\theta`)

`\cos \theta = (30)/(50) = 0.6`

or

`\theta = \cos^(-1) (0.6)`

Simplify:

`\theta = 53.13^(\circ)`

Therefore, the angle of elevation to the closest degree of the ladder is 51.13 degree