A ladder is leaning against a house. the distance from the bottom base of the ladder to the house is 12 feet. Write an equation to determine the length of the ladder.

Question

Let y = the length of the ladder. Let x = the measure of the angle formed by the ladder and the ground. Determine the distance when the measure of the angle is 30 degrees.

Answer 1

Pythagorus theorem:

The distance from the bottom base of the ladder to the house is 12 feet.

Let the distance from the base of the house to the top of the ladder touching the house be X.

Let the length of the ladder be Z.

Using the theorem:

X²+12² = Z²

X² - Z² = -144

Answer 2

cos(x) = adjacent/hypotenuse = 12/y

So y = 12/cos(x)