Question

Mark leaned a 12 foot ladder against the side of his house.The bottom of the ladder was 4 feet from the house. How far up the house was the top of the ladder?

Answer 1

If you stand over there at the end of the house and look back here
at the ladder, you'll see that what Mark has is a right triangle.

There's a right angle where the side of the house meets the ground,
the base of the triangle is the 4 feet, and the ladder is the hypotenuse.
So we know that

(length of the ladder)² = (4-ft)² + (height of the top of the ladder)²

(12-ft)² = (4-ft)² + (height of the top of the ladder)²

(144 ft²) = (16 ft²) + (height of the top of the ladder)²

Subtract 16ft² from each side, and you have:

128 ft² = (height of the ladder)²

Take the square root of each side:

Height of the ladder = √(128 ft²) = 11.31 ft. (rounded)