Question

The angle of elevation of a ladder leaning against a vertical wall is 60°, and the foot of the ladder is 9.6 m from the wall. Find the length of the ladder.

Answer 1

Given: Angle of elevation = 60°, distance from wall (foot) = 9.6 m, ladder length = L (hypotenuse).

Step-wise calculation:

1. In the right triangle,

`cos (60^circ) = "Adjacent"/"Hypotenuse"` 

= `9.6/L`

2. `cos (60^circ) = 1/2`

So, `1/2 = 9.6/L`.

3. Solve for L:

`L = 9.6 ÷ 1/2`

= 9.6 × 2

= 19.2 m

The length of the ladder is 19.2 m.