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: [tex]\cos\theta=\frac{Adjacent\ side}{Hypotenuse}[/tex]
In Δ ABC
[tex]\cos85.5\°=\frac{AC}{AB}[/tex]
Multiplying both sides by AB.
[tex]AB\cos 85.5\°=\frac{AC}{AB}\times AB[/tex]
[tex]AB\cos 85.5\°=AC[/tex]
[tex]AC=AB\cos 85.5\°[/tex]
Substituting value of AB and cos 85.5°
[tex]AC=94\cos 85.5\°[/tex]
∴ [tex]AC=7.38\ ft[/tex]
Distance of the keys on ground from the base of the tower = 7.38 ft
