Question

In this picture, the dotted line represents a ladder. How high on the house for the ladder reach?

Answer 1

According to the image there is a ladder leaning against the wall of the house, however both the floor of the house and the bottom of the ladder are leveled equal, which means they will form a right triangle between both of them that looks like this:

when we are solving right triangles we can use the trigonometric functions when one side and an angle is given or the pythagorean if the other two sides ar given in order to find the missing side.

Since the exercise is given the length of the ladder and how far it is from the house we can use the pythagorean theorem to find the heigth of the house the ladder reaches.

`a^2+b^2=c^2`

in which c is the longest side of the triangle, in this case it is the ladders length, 20ft.

write the equation

`a^2+4^2=20^2`

solve the equation for a

`\begin{gathered} a^2=20^2-4^2 \\ a^2=400-16 \\ a^2=384 \\ a=\sqrt[]{384} \\ a=19.5959\approx19.60ft \end{gathered}`

the ladder reaches about 19.60 ft of the house's height.