Question

A ladder leaning against a vertical wall makes an angle of 30° with ground. The foot of the ladder is 3 m from the wall. Determine the length of the ladder.

Answer 1

Given:

Angle between ladder and ground = 30°

Distance from foot of ladder to wall = 3 m

Let L = Length of the ladder.

Step-wise calculation:

1. In the right triangle. 

`cos 30^circ = "Adjacent"/"Hypotenuse"`

= `3/L`

2. `cos 30^circ = sqrt(3)/2`

So, `sqrt(3)/2 = 3/L`.

3. Solve for L:

`L = 3 xx 2/sqrt(3)`

= `6/sqrt(3)`

= `2sqrt(3)`

4. Numeric value:

`2sqrt(3) ≈ 3.4641` m

Length of the ladder = `2sqrt(3)` m ≈ 3.464 m.