Question: Find the missing side length of the following right triangles. b) \[ \begin{array}{c}…

Find the missing side length of the following right triangles.

b)

\[ \begin{array}{c} \text{i} \\ \hline \end{array} \]

\[ \begin{array}{c} 30 \text{ ft} \\ \hline \end{array} \]

\[ \begin{array}{c} 27.6 \text{ ft} \\ \hline \end{array} \]

Solution

To find the missing side length of the right triangle, we can use the Pythagorean theorem. The theorem states: \[ a^2 + b^2 = c^2 \] where \(c\) is the hypotenuse. In this triangle, the hypotenuse is the side labeled 30 ft, and the other sides are 27.6 ft and the missing side \(i\). Substitute the known values: \[ i^2 + 27.6^2 = 30^2 \] Calculate \(30^2\): \[ 30^2 = 900 \] Calculate \(27.6^2\): \[ 27.6^2 = 761.76 \] Substitute back into the equation: \[ i^2 + 761.76 = 900 \] Subtract 761.76 from both sides: \[ i^2 = 138.24 \] Take the square root of both sides: \[ i = \sqrt{138.24} \] Calculate the square root: \[ i \approx 11.76 \] So, the missing side length \(i\) is approximately 11.76 ft.