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).
[tex]\sin\theta = \frac{Opposite\ side}{Hypotenuse}[/tex]
[tex]\sin C=\frac{AB}{AC}[/tex]
Plugging in values.
[tex]\sin 51.5\°=\frac{22}{AC}[/tex]
Multiplying AC both sides.
[tex]AC\sin 51.5\°=\frac{22}{AC}\times AC[/tex]
[tex]AC\sin 51.5\°=22[/tex]
Dividing both sides by [tex]\sin 51.5\°[/tex]
[tex]\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=28.1\ ft[/tex]
Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.
