Question

Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. Label each with the information you know. ( the tower is 65.6 feet tall and leans to the left at 7.1 degrees).

Answer 1

Answer: The keys landed 8.1 feet away from the base of the tower.

Explanation:

The tower is tilted a bit to the left, the length of the tower is 65.6 ft and it is tilted by 7.1 degrees

Then we can think the length of the tower as the hypotenuse of a triangle rectangle, the distance between the point of the tower and the ground will be the adjacent cathetus of the triangle rectangle:

by the relation:

cos(7.1°) = X/65.6ft

X = cos(7.1°)*65.6ft = 65.1 ft

and this line is the trajectory that the keys travel.

The distance between the base of the tower and the point where the keys land will be the opposite cathetus to the angle of 7.1 degrees, and we can find it by:

sin(7.1°) = Y/65.6ft

Y = sin(7.1°)*65.6ft = 8.1 ft

Answer 2

The keys landed 8.11 feet from the base of the tower.

Explanation:

Let after landing on the ground x be the distance of keys from the base of the tower,

Given, the height of the tower = 65.6 feet,

And, it leans to the left at 7.1 degrees,

So, the angle made by tower to the vertical line = 71°

Thus, by making the diagram of the given situation,

We can write,

`sin 7.1^(\circ)=(x)/(65.6)` (
`sin \theta = (Perpendicular)/(Base)` )

`65.6* sin 7.1^(\circ)=x`

`\implies x = 8.10825687418\approx 8.11`

Hence, the keys landed 8.11 feet from the base of the tower.