Ladder angle h x d x 30 ft What is the distance d, from the base of the building to the bottom of this 30-foot ladder when the top of the ladder reaches a height, h, of 28 feet on the building's wall?

Question

Please help the only available answers are

1.4 feet

41 feet

10.8 feet

and

2 feet

Answer 1

Hello Laia,

As I suspect you are aware this is a Pythagorean theorem problem. I always recommend to my students in classes to draw the information given to make it easier to solve.

Since I cannot draw this for you, let me explain the way the right angle is situated. The right angle is located at the bottom of the building where it reaches the building.

We know the top of the ladder reaches a height of 28 feet and we know the hypotenuse of this right angle is unknown. Therefore, the missing value is the distance from the building to the ladder at the base and this creates the following equation:

a² + b² = c²

We already know the leg of this right triangle is unknown. But we do know the hypotenuse is 30, and the height - which provides the final leg is 28 feet. Now, let's substitute the values.

a² + b² = c²

a² + 28² = 30²

a² + 784 = 900

a² = 116

a = √116

a ≈ 10.77

When rounded, you can see that the answer now becomes 10.8 feet.

I hope I have helped and you have a great week. Best.