Question

A ladder is leaning against a wall and it makes an angle of 60 with the horizontal.

The foot of the ladder is 50 m away from the wall.

Find the length, l, of the ladder.

Answer 1

The length, l, of the ladder is 100 meters

Explanation:

The given scenario forms a right triangle in which the length of ladder is hypotenuse, the distance between the foot of the ladder and the wall is base(as shown in attached diagram) We have to find length of ladder(l)

For this purpose trigonometric ratios can be used. The ratio which includes both base and hypotenuse of triangle is cos θ where θ = 60°

So,

`cos\ 60 = (50)/(l)`

The value of cos 60 is 1/2 or 0.5

So,

`0.5 = (50)/(l)\\l = (50)/(0.5)\\l = 100`

Hence,

The length, l, of the ladder is 100 meters