Question

b) calculate the percent grade of the ramp to the nearest percent
c) show the pitch to the ramp in ratio form
(image of a right triangle with hypotenuse 13 m, base 12 m)

Explanation:

Part b)

Step 1: Find the height of the ramp (using Pythagoras)

The ramp is the hypotenuse (\(c = 13\) m) and the horizontal distance is \(b = 12\) m. Let the height be \(a\). By Pythagoras' theorem \(a^{2}+b^{2}=c^{2}\), so \(a=\sqrt{c^{2}-b^{2}}\).
\(a=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25} = 5\) m.

Step 2: Calculate percent grade

Percent grade is \(\frac{\text{height}}{\text{horizontal distance}}\times100\%\). So \(\frac{5}{12}\times100\%\approx41.67\%\), rounded to nearest percent is \(42\%\).

Part c)

Pitch is the ratio of height to horizontal distance. So the ratio is \(5:12\) (height : horizontal distance) or \(\frac{5}{12}\) (height over horizontal distance).

Part b) Answer: \(42\%\)

Part c) Answer: \(5:12\) (or \(\frac{5}{12}\))

Answer:

Pitch is the ratio of height to horizontal distance. So the ratio is \(5:12\) (height : horizontal distance) or \(\frac{5}{12}\) (height over horizontal distance).

Part b) Answer: \(42\%\)

Part c) Answer: \(5:12\) (or \(\frac{5}{12}\))