Calculate the Angle of a Ramp
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1. Whaikaha (Ministry of Disabled People) says: "A ramp needs to slope gently (meaning it has a slope of no more than 1 metre rise to every 12 metres of length) to make it safe and easy to use". If a ramp has this slope, what angle would the ramp make with the ground?
This question includes visual content: The image consists of two parts: a photograph of a house with a wooden deck and a ramp, showing a height of 60 cm, and a schematic right-angled triangle below it. The triangle has a vertical side labeled '1 m' and a horizontal side labeled '12 m'. An angle 'x' is marked at the vertex where the hypotenuse meets the horizontal base. A right angle symbol is present at the corner between the vertical and horizontal sides.
Animated Video Solution
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Step by Step Written Solution
Hi Keita, let's solve this together by finding the angle that a ramp with this gentle slope makes with the ground.
Slope Guideline Analysis
Let's represent this ramp using a right-angled triangle where the horizontal length is twelve meters and the vertical rise is one meter.
Right Triangle Model
We want to find the angle x. Since we have the opposite side and the adjacent side, we can use the tangent ratio.
Trigonometric Ratio
The tangent of angle x is defined as the length of the opposite side divided by the length of the adjacent side.
Now, let's substitute our known values into the formula.
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