Question: 2. Use the Pythagorean theorem to find the missing side length of the triangle. a) \[…

2. Use the Pythagorean theorem to find the missing side length of the triangle.

a) \[ \begin{array}{c} \text{hyp} \\ \text{f} \\ \text{13 in} \\ \text{18 in} \\ \text{adj} \end{array} \]

b) \[ \begin{array}{c} \text{i} \\ \text{30 ft} \end{array} \]

Solution

To solve the problem using the Pythagorean theorem, we need to find the missing side length \( f \) of the right triangle. The Pythagorean theorem states: \[ a^2 + b^2 = c^2 \] where \( c \) is the hypotenuse. Here, we have: - \( a = 13 \) inches - \( b = 18 \) inches We need to find the hypotenuse \( f \). Plug the values into the equation: \[ 13^2 + 18^2 = f^2 \] Calculate the squares: \[ 169 + 324 = f^2 \] Add the numbers: \[ 493 = f^2 \] Take the square root of both sides to find \( f \): \[ f = \sqrt{493} \] Calculate the square root: \[ f \approx 22.2 \] So, the missing side length \( f \) is approximately 22.2 inches.