Question

Noah wants to clean his second story windows and plans to buy a ladder that will reach at least

22


feet high. If he leans the ladder against the house so that the base of the ladder makes a


51.5


∘


angle with the ground, how long of a ladder should he buy? Please round to one decimal place

Answer 1

Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.

Explanation:

Given:

Noah has to reach at least 22 ft height.

Angle made by the base of ladder with the ground = 51.5°

To find the length of the ladder.

Solution:

On drawing the situation, we get a right triangle. The hypotenuse of the triangle represents the length of the ladder.

In triangle ABC.

∠C = 51.5°

AB = 22 ft

Applying trigonometric ratio to find AC (length of the ladder).

`\sin\theta = (Opposite\ side)/(Hypotenuse)`

`\sin C=(AB)/(AC)`

Plugging in values.

`\sin 51.5\°=(22)/(AC)`

Multiplying AC both sides.

`AC\sin 51.5\°=(22)/(AC)* AC`

`AC\sin 51.5\°=22`

Dividing both sides by
`\sin 51.5\°`

`(AC\sin 51.5\°)/(\sin 51.5\°)=(22)/(\sin 51.5\°)`

`AC=(22)/(\sin 51.5\°)`

`AC=28.1\ ft`

Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.