Question

A 17-foot ladder is placed against a wall. The base of the ladder is

8 feet from the wall. How high up the wall does the ladder reach?

Answer 1

h^2 + 64 = 289

Answer 2

or, learn to recognize some basic Pythagorean triples, such as 8-15-17

Answer 3

[AI-generated answer — Explain Bot]

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the ladder is the hypotenuse, and the base of the ladder (8 feet) is one of the other two sides. Let's call the height up the wall that the ladder reaches "h".

According to the Pythagorean theorem, we have:

(8^2) + (h^2) = (17^2)

Simplifying this equation, we have:

64 + h^2 = 289

Now, let's isolate the h^2 term by subtracting 64 from both sides:

h^2 = 289 - 64

h^2 = 225

To find the height h, we take the square root of both sides:

√(h^2) = √225

h = 15

Therefore, the ladder reaches a height of 15 feet up the wall.