Question

Dillon places a ladder against a wall. The base of the ladder is 8 feet from the wall, and the ladder is 30 feet long. How high will the ladder reach, in feet?

A) 22 feet
B) 15 feet
C) 28 feet
D) 10 feet

Answer 1

Using the Pythagorean theorem to solve for the height the ladder reaches, we find it is approximately 28 feet from the ground. The closest answer choice is C) 28 feet.

Step-by-step explanation:

To find out how high the ladder will reach, you can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this problem, the ladder is the hypotenuse, the distance from the wall to the base of the ladder is one leg, and the height reached by the ladder is the other leg.

The Pythagorean theorem is stated as a2 + b2 = c2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. In this case, we have:

• Length of the ladder (c): 30 feet
• Distance from the wall to the base of the ladder (a): 8 feet
• The height the ladder will reach (b): ?

Plugging into the formula, we have:

82 + b2 = 302

64 + b2 = 900

Now, solve for b2:

b2 = 900 - 64

b2 = 836

And taking the square root:

b = sqrt(836)

b = 28.94, which rounds to 29 feet.

The closest answer that fits the provided options is 28 feet (Choice C).