A 10 foot ladder is placed against a building if the base of the ladder is 6 feet away from the building how far up the building will the ladder reach

Answer 1

Placing a ladder up against a building will create a right triangle, with the legs being the ground and the building and the hypotenuse being the ladder. Since we have a right triangle and we know two sides, we can use the Pythagorean Theorem to solve for the 3rd:

6²+b²=10²

36+b²=100

b²=64

b=8

So the ladder will reach 8 feet up.

Hope this helps!

Answer 2

With the ladder leaning at the wall, the wall and the ground form a right angle. That makes the ladder the hypotenuse of a right triangle. As such the Pythagorean Theorem a² + b² = c² applies.

Since we know c = 10 and can assign the distance of the base of the ladder from the wall to either a or b we can no write our equation as follows:

6² + b² = 10²

36 + b² = 100 | -36

b² = 64 | √

b = √64

b = 8

The ladder will reach 8 feet up the wall.