Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 72° when the bottom of the ladder is 14 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

Answer 1

Answer:

Length of ladder = 45.30 ft

Step-by-step explanation:

Given data:

Distance between the bottom of the ladder and side of house = 14 ft

Angle of elevation of the ladder = 72°

To find length of the ladder.

From the data given to us we can construct a right triangle ABC.

For the Δ ABC

AC= 14 ft

∠A= 72°

We can apply trigonometric ratio to find side AB which is the length of the ladder.

$\cos72\°=\frac{AC}{AB}$        [ ∵ $\cos\theta=\frac{Adjacent\ side}{Hypotenuse}$ ]

Multiplying both sides by AB.

$AB\cos72\°=\frac{AC}{AB}\times AB$

$AB\cos72\°=AC$

Dividing both sides by cos72°

$\frac{AB\cos72\°}{cos72\°}=\frac{AC}{cos72\°}$

$AB=\frac{AC}{cos72\°}$

Substituting value of AC and cos 72°

$AB=\frac{14}{0.309}$

$AB=45.30\ ft$

Thus, length of the ladder = 45.30 ft