Question

question 13: (technology required.) ramps in a parking garage need to be both steep and safe. the maximum safe incline for a ramp is 8.5 degrees. is this a safe ramp? explain or show your reasoning.

Explanation:

Step1: Identify the triangle type

We have a right - triangle where the opposite side to the angle of inclination (let's call the angle \(\theta\)) is \(20\) and the hypotenuse is \(100\). We can use the sine function, which is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Calculate the angle of inclination

Using the formula \(\sin\theta = \frac{20}{100}=0.2\). Then we find \(\theta=\arcsin(0.2)\). Using a calculator, \(\arcsin(0.2)\approx11.54^{\circ}\).

Step3: Compare with the given angle

The given maximum safe angle is \(8.5^{\circ}\). Since \(11.54^{\circ}>8.5^{\circ}\), the ramp is not safe.

Answer:

The ramp is not safe because the calculated angle of inclination (\(\approx11.54^{\circ}\)) is greater than the maximum safe angle of \(8.5^{\circ}\).