Question

Jaquira wanted to set a ladder against the house to change a light above the garage. The ladder was 19 feet long, and reached the light, which was 7 feet above the ground. What was the distance from the base of the ladder to the house? Round to the nearest tenth.

Answer 1

Answer:
`17.7\ feet`

Explanation:

Draw a right triangle as the one shown attached.

In order to calculate the distance from the base of the ladder to the house, you can use the Pythagorean Theorem:

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

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Solving for one of the legs:

`b=√(a^2-c^2)`

You can notice that:

`a=19\ ft\\c=7\ ft\\b=x`

Therefore, substituting values into
`b=√(a^2-c^2)`, you get that the distance from the base of the ladder to the house, rounded to the nearest tenth, is:

`x=√((19\ ft)^2-(7\ ft)^2)\\\\x=17.7\ ft`