Question

A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach.

Answer 1

Answer: $7\sqrt{2}$ feet

Step-by-step explanation:

This question uses special right triangles.

There are two main special triangles to remember.

Attached is a diagram of the triangle. Both the base and the height are the same, so the 14 foot-long ladder is the hypotenuse.

The hypotenuse of a 45-45-90 triangle is equal to $\sqrt{2} *k$, where k is the side length.

We can solve for the side lengths by using this equation:

$14 = \sqrt{2} *k$

Simplifying this equation by dividing both sides by the square root of 2 and rationalizing the denominator, we get

$7\sqrt{2} =k$

Your side length of the height of the triangle is equal to 7 times the square root of 2.