Question

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

Answer 1

Answer:

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

Step-by-step 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).

$\sin\theta = \frac{Opposite\ side}{Hypotenuse}$

$\sin C=\frac{AB}{AC}$

Plugging in values.

$\sin 51.5\°=\frac{22}{AC}$

Multiplying AC both sides.

$AC\sin 51.5\°=\frac{22}{AC}\times AC$

$AC\sin 51.5\°=22$

Dividing both sides by $\sin 51.5\°$

$\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}$

$AC=\frac{22}{\sin 51.5\°}$

$AC=28.1\ ft$

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