In Alberta, ramps that are designed for people using mobility devices must meet certain safety requirments. One such requirment is that the angle between the ramp and the horizontal must be less than 4.8°. Explain whether or not the ramp below is acceptable.

The 3 angles inside a triangle must add up to 180, so we just need to subtract the known angles from 180 and see what we have left.

Given $94.7^{\circ}$94.7^{?}at the top, we must first find the angle inside the triangle. They are on the same straight line so they add up to 180 as well.

180-94.7=85.3

So inside the triangle we have, $90^{\circ}$90^{?} , $85.3^{\circ}$85.3^{?} and our mystery angle.

$180-90-85.3=4.7^{\circ}$180−90−85.3=4.7^{?}

which is less than 4.8, so the ramp meets the safety criteria

3 years ago

## Answered By Alireza R

$\angle A+\angle B+\angle C1=180$∠A+∠B+∠C1=180

$\angle C1+\angle C2=180$∠C1+∠C2=180

$\therefore$∴ $\angle C2=\angle A+\angle B$∠C2=∠A+∠B (1)

In this case, $\angle C2=94.7°$∠C2=94.7°

Having said that $\angle B=90°$∠B=90° and solving (1), $\angle A=4.7°$∠A=4.7° which is less than 4.8° allowable maximum. So the ramp is acceptable.

## Attached Whiteboard:

Play Drawing3 years ago

## Answered By Clifton P

The 3 angles inside a triangle must add up to 180, so we just need to subtract the known angles from 180 and see what we have left.

Given $94.7^{\circ}$94.7

^{?}at the top, we must first find the angle inside the triangle. They are on the same straight line so they add up to 180 as well.180-94.7=85.3

So inside the triangle we have, $90^{\circ}$90

^{?}, $85.3^{\circ}$85.3^{?}and our mystery angle.$180-90-85.3=4.7^{\circ}$180−90−85.3=4.7

^{?}which is less than 4.8, so the ramp meets the safety criteria