Question

If a 10-foot ladder is leaning against a wall so that the foot of the ladder is 6 feet from the base of the wall, how far up the wall will the ladder reach?

A) 4 feet
B) 6 feet
C) 8 feet
D) 10 feet

Answer 1

The ladder will reach a distance of 8 feet up the wall.

Step-by-step explanation:

The ladder forms a right triangle with the wall and the ground. The length of the ladder is the hypotenuse of the triangle, and the distance from the foot of the ladder to the wall is one of the legs. Using the Pythagorean theorem, we can find the length of the other leg, which represents how far up the wall the ladder will reach.

Let's use the Pythagorean theorem:

a^2 + b^2 = c^2

where 'a' is the distance from the foot of the ladder to the wall, 'b' is the distance up the wall that the ladder reaches, and 'c' is the length of the ladder.

Plugging in the values, we have:

6^2 + b^2 = 10^2

Simplifying the equation:

36 + b^2 = 100

Subtracting 36 from both sides:

b^2 = 64

Therefore, the ladder will reach a distance of 8 feet up the wall.