Question

A ladder 8ft long resting against a house makes a 60 degree

angle with the ground. how far up does the house reach? give answer
in terms of radicals with the radical in the numerator.

Answer 1

4√3 feet

Explanation:

Here, a ladder is resting against a house makes a 60° with the ground,

Consider x be the distance of the top of ladder from the foot of house and y be the distance of bottom of ladder from the house. ( shown in the below diagram )

Using trigonometric ratio,

`\sin 60^(\circ)=\frac{\text{Distance of top of ladder from the bottom of house}}{\text{Length of ladder}}`

We have, length of ladder = 8 ft,

`\sin 60^(\circ)=(x)/(8)`

`(√(3))/(2)=(x)/(8)`

`8√(3) = 2x`

`4√(3)=x`

Hence, the house would reach 4√3 feet up.