The top of the slide is 7 feet from the ground and has an angle of depression of \( 23^{\circ} \). What is the length of the slide, \( x \) (₹o at least the nearest hundredth)? \( x=\frac{\mathrm{ft}}{\text { Basic Funcs Trig }} \)

To find the length of the slide, you can use the angle of depression and a little basic trigonometry. The angle of depression forms a right triangle with the height of the slide as one side. Here we have the height (opposite side) at 7 feet and the angle \( 23^{\circ} \). You can use the sine function, which relates the opposite side to the hypotenuse: \[ \sin(23^{\circ}) = \frac{7}{x} \] Rearranging gives you: \[ x = \frac{7}{\sin(23^{\circ})} \] Calculating \(\sin(23^{\circ})\) and substituting gives you the length \( x \). This will help you find the slide’s actual length! After doing the math, the length of the slide is approximately \( x \approx 29.72 \text{ ft} \) when rounded to the nearest hundredth. So grab your calculator and ride down that slide in your mind!