Question

A right triangle shows the base with a value of 3, the hypotenuse on the left with a value of 15, and the perpendicular side to the base on the right with a question mark.

Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.

Answer 1

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, the unknown side length, which is the perpendicular side to the base, represents one of the shorter sides.

Let's denote the unknown side length as $x$. We can set up the equation as follows:

$3^2 + x^2 = 15^2$

$9 + x^2 = 225$

$x^2 = 225 - 9$

$x^2 = 216$

$x = \sqrt{216}$

$x \approx 14.7$

Therefore, the unknown side length is approximately 14.7 units when rounded to the nearest tenth.