Question

The leaning tower of niles is 94 feet high and makes an angle of 85.5 degrees from the ground to the top of the tower. If you drop keys from the top of the tower how far from the base of the tower would they land?

Answer 1

Answer:

Distance of the keys on ground from the base of the tower = 7.38 ft

Step-by-step explanation:

Given:

Height of tower = 94 ft

Tower is leaning and makes an angle of 85.5 degrees from the ground.

Keys are dropped from the top of the tower.

To find the distance of the keys on ground from the base of the tower.

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

For the Δ ABC

AB= 94 ft

∠A= 85.5°

We can apply trigonometric ratio to find side BC which is  the distance of the keys on ground from the base of the tower.

Using cosine ratio: $\cos\theta=\frac{Adjacent\ side}{Hypotenuse}$

In Δ ABC

$\cos85.5\°=\frac{AC}{AB}$

Multiplying both sides by AB.

$AB\cos 85.5\°=\frac{AC}{AB}\times AB$

$AB\cos 85.5\°=AC$

$AC=AB\cos 85.5\°$

Substituting value of AB and cos 85.5°

$AC=94\cos 85.5\°$

∴ $AC=7.38\ ft$

Distance of the keys on ground from the base of the tower = 7.38 ft