Question

A 50 foot ladder is set against the side of a house so that it reaches up 40 feet. If Aisha grabs the ladder at its base and pulls it 9 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 31 ft Round to the nearest tent )

Answer 1

Answer: 31.3 feet

Explanation: In this case we will have two triangles.

The first and the second has the hypotenuse of 50 feet.

Using the Pythagorean theorem we have the following equations.

`50^(2) = 40^(2) + x^(2)`

`50^(2) = y^(2) + (x+9)^(2)`

Solving the first equation we get

`x = \sqrt{ 50^(2) - 40^(2)`

`x = 30` feet

Also, so you know, the 3:4:5 rule could've been applied to make it faster.

`y^(2) = 50^(2) - 39^(2)`