Question

A ladder is leaning up against a house. The ladder is 20 feet long and the base of the ladder is 12 feet away from the house. How far up the house can the ladder reach?

Answer 1

Answer:

16 feet

Step-by-step explanation:

The length of the ladder=20 feet

Distance from the base of the ladder to the house = 12 feet

You will notice that a wall is vertical and the ladder makes an angle with the horizontal ground(making it the hypotenuse). This is a right triangle problem.

To find the how far up the house can the ladder can reach, we simply find the third side of the right triangle.

From Pythagoras theorem

$Hyp^2=Opp^2+Adj^2\\20^2=12^2+Adj^2\\Adj^2=400-144\\Adj^2=256\\Adj=\sqrt{256}=16$

The third side of the right triangle is 16. Therefore the ladder leans 16 feet from the ground.

Answer 2

Answer:

16 feet

Step-by-step explanation:

the height of the ladder, the distance from the ladder base to the house and the height of the house the ladder will reach will form a triangle, as shown in the image.

To know the height of the house the ladder will reach, we just need to use Pythagorean theorem. Being h the house's height we want, we have:

20^2 = 12^2 + h^2

h^2 = 400 - 144 = 256

h = 16 feet.