Question

Clayton is responsible for changing the broken light bulb in a street lamp. The street lamp is 12 ft high. Clayton places the base of his ladder 4 feet from the base of the street lamp. Clayton can extend his ladder 10 feet to 14 feet. How long must his ladder be to reach the top of the street lamp? Will Clayton's ladder work? Round your answer to the nearest tenth.

Answer 1

Explanation:

The ladder forms a right angle triangle with the street lamp and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the street lamp represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the street lamp represents the adjacent side of the right angle triangle.

To determine how long, h his ladder must be to reach the top of the street lamp, we would apply

Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

h² = 12² + 4² = 144 + 16

h² = 160

h = √160

h = 12.7 ft

Yes, his ladder will work. He should place it at 12.7 feet