A 5 foot latter is leaning against the house. The bottom of the ladder is leaning 3 feet away from the house. How high up is the top of the ladder on the house?

Answer: the top of the ladder is 4ft above the ground.

Step-by-step explanation:

The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.

The length of the ladder represents the hypotenuse of the right angle triangle.

The ground distance from the base of the house of the foot of the ladder represents the adjacent side of the right angle triangle.

Therefore, to determine high up is the top of the ladder on the house, x, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

5² = x² + 3²

25 = x² + 9

x² = 25 - 9 = 16

x = √16 = 4