Question: f) \[ \begin{array}{c} \text{opp} \\ 3.94 \text{ ft} \end{array} \] \[ \begin{array}{c}…

f)

\[ \begin{array}{c} \text{opp} \\ 3.94 \text{ ft} \end{array} \]

\[ \begin{array}{c} \text{hyp} \\ h \end{array} \]

\[ 23^\circ \]

\[ \begin{array}{c} \text{adj} \end{array} \]

Solution

To solve the problem, we need to find the hypotenuse \( h \) of the right triangle. We are given: - The opposite side is 3.94 ft. - The angle is \( 23^\circ \). We can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse. The formula is: \[ \sin(23^\circ) = \frac{3.94}{h} \] Rearrange the equation to solve for \( h \): \[ h = \frac{3.94}{\sin(23^\circ)} \] Calculate \( h \): \[ h \approx \frac{3.94}{0.3907} \approx 10.08 \text{ ft} \] Thus, the hypotenuse \( h \) is approximately 10.08 ft.