Question

A 12 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 ?

A. 24√2
B.6√2
C. 6 feet
D.12√2

Answer 1

The answer is B. 6 square root 2

Explanation:

Answer 2

If the ladder makes a 45 degree angle with the building, then it also makes a 45 degree angle with the ground (45-45-90). The rule for the 45-45-90 is (x, x, xsqrt2). The sqrt2 is the hypotenuse measure, which is always the longest of the sides in a right triangle. If the hypotenuse is 12, set up your equation like this:
`12=x \sqrt2` In order to undo that square root, square both sides, getting
`144=2 x^(2)` Now divide both sides by 2 to get
`72= x^(2)` and take the square root of both sides and simplify. The square root of 72 simplified is
`6 \sqrt2`