Question

A 200 foot wire is attached from the top of a tower to a point on the ground 40 feet from the base of the tower. Find the height of the tower to the nearest foot. A) 158 feet B) 160 feet C) 196 feet D) 384 feet

Answer 1

200^2 = 40^2 + b^2
40000 = 1600 + b^2
38400 = b^2
b = 196 ft (c)

Answer 2

The height of the tower is 196 feet .

Option (C) is correct .

Explanation:

By using the pythagoream theorem

Hypotenuse² = Perpendicular² + Base²

As given

A 200 foot wire is attached from the top of a tower to a point on the ground 40 feet from the base of the tower.

As the diagram is given below .

Hypotenuse= AB = 200 feet

Base = CB = 40 feet

Perpendicular = AC

Put all the value in the above

200² = 40² + AC²

40000 = 1600 + AC²

AC² = 40000 - 1600

AC² = 38400

AC = √38400

AC = 196 feet (Approx)

Therefore the height of the tower is 196 feet .

Option (C) is correct .