math question help

Question

A building is 11 ft from a 12-ft fence that surrounds the property. A worker wants to wash a window in the building 15 ft from the ground. He plans to place a ladder over the fence so it rests against the building.? He decides he should place the ladder 7 ft from the fence for stability. To the nearest tenth of a? foot, how long a ladder will he? need?

 

he will need a ____ft ladder

Answer 1

It's best to draw a picture to understand what's going on here. Note that the height of the fence is irrelevant in this problem.

 

This is a Pythagorean theorem problem

 

Let a = the horizontal distance from the building to the base of the ladder

Let b = the vertical distance from the ground to the top of the ladder

Let c = the length of the ladder

 

The problem says that the base of the ladder is 7ft outside the fence, and that the fence is 11 ft from the building.

Therefore, we know that a = 11 + 7 = 18 ft

 

The problem says that the window is 15 ft from the ground, so we know that b = 15ft

 

So we are solving for the hypotenuse of a right triangle with a = 18 and b = 15

 

a² + b² = c²

18² + 15² = c²

 

Now we solve for c:

 

324 + 225 = c²

549 = c²

c = √(549)

c ≈ 23.4307

 

Therefore the ladder must be 23.4 ft long.