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: $17.7\ feet$

Step-by-step 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:

$b=\sqrt{a^2-c^2}$

You can notice that:

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

Therefore, substituting values into $b=\sqrt{a^2-c^2}$, you get that the distance from the base of the ladder to the house, rounded to the nearest tenth, is:

$x=\sqrt{(19\ ft)^2-(7\ ft)^2}\\\\x=17.7\ ft$