Final answer:
The length of the base of the right triangle is approximately 13.9 inches, which is found by applying the Pythagorean theorem and taking the square root of the difference between the square of the hypotenuse and the square of the height.
Step-by-step explanation:
To find the length of the base of a right triangle when we know the length of the hypotenuse (19 inches) and the height (13 inches), we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The formula for the Pythagorean theorem is:
a² + b² = c²
Here, c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Let's call the length of the base b and the height a. We can rearrange the formula to solve for b:
b² = c² - a²
Plugging in the known values we get:
b² = 19² - 13²
b² = 361 - 169
b² = 192
Now we take the square root of both sides:
b = √192
b ≈ 13.9 inches (using a calculator)
Therefore, the length of the base of the triangle is approximately 13.9 inches.