An accessibility ramp slopes upward at an angle of 7.5^circ After traveling a horizontal distance of 80 feet,what is the vertical change? What is the length of the ramp? Draw and label a diagram.Round I answers to nearest foot. Vertical change: __ Length of ramp: __

## Step 1: Diagram and Variable Definition<br />### We draw a right triangle representing the ramp, where the horizontal distance is 80 ft, the angle of elevation is $7.5^{\circ}$, and we need to find the vertical change (opposite side) and the ramp length (hypotenuse). Let's denote the vertical change as $y$ and the ramp length as $r$.<br /><br />## Step 2: Calculating the Vertical Change<br />### We use the tangent function: $\tan(7.5^{\circ}) = \frac{y}{80}$. Solving for $y$, we get $y = 80 \times \tan(7.5^{\circ}) \approx 10.5$ ft.<br /><br />## Step 3: Calculating the Ramp Length<br />### We use the cosine function: $\cos(7.5^{\circ}) = \frac{80}{r}$. Solving for $r$, we get $r = \frac{80}{\cos(7.5^{\circ})} \approx 80.7$ ft.