Algebra word problems

Question

A -foot ladder is leaning against a building. The base of the ladder is  feet from the side of the building. How high does the ladder reach along the side of the building? lost you in the math part of your equation, not sure how you go the 10 and 15

Answer 1

Hello, Bridget,

The problem is asking the height of what is a right triangle system. Imagine the right angle at the base of the building. I'll call the vertical distance up from that point as the height, or H. We want to find H, the distance the ladder reaches up the building. The distance along the ground to where the ladder is resting, I'll call the base, or B. The ladder itself becomes the hypotenuse in this diagram, which I'll label as C..

Since it is a right angle, we know that H² + B² = C².

H = the unknown

B = 12 ft

C = 20 ft

Thus, H² + (12)² = (20)²

H² = 400 - 144

H = 16 feet

Fun!

I hope this helps,

Bob

Answer 2

the ladder, base and building form a right triangle with hypotenuse =20 and one side = 12

the height is the other side = sqr(20^2 - 12^2) = sqr (400- 144) = sqr (256) = 16 feet

It's a 20-16-12 right triangle

or a 5-4-3 right triangle, a common right triangle with integer sides

the hypotenuse squared = the sum of squares of the other 2 sides

20 squared = 12 squared + 16 squared

400 = 144 + 256