Question

A ramp is used to load a snowmobile onto the back of a pickup truck. The truck bed is 1.3m above the ground. For safety, the angle of the ramp should be less than 40°. What is the shortest possible length of the ramp to the nearest centimetre? Explain why.

Answer 1

Answer:

2.02 m

or 2 m 2 cm

Step-by-step explanation:

Imagine a triangle containing the 40° angle and that this angle is at the left.  Then the height of the truck bed is 1.3 m and the "shortest possible length of the ramp" is the hypotenuse of this triangle.  We need to find the length of this ramp, that is, the length of the hypotenuse.  

The sine function relates this 40° angle and the 1.3 m height of the truck bed:

sin 40° = opp / hyp = 1.3 m / hyp

which can be solved for 'hyp' as follows:

              1.3 m

hyp = ----------------- = (1.3 m) / 0.6428)

             sin 40°

                                                                                  1.3 m

Thus, the length of the ramp must be less than -------------- or 2.02 m

                                                                                 0.6428

where this last result is to the nearest cm.

If the ramp is shorter the angle of the ramp will be smaller and the ramp angle considered safer.