Question

3.A ramp is made using a board. The board is 12 ft long. The ramp is 3 ft high. What angle does the ramp make with the ground? (this would be finding the angle of elevation) Round your answer to the nearest tenth of a degree.

Draw a diagram (1 point). Set up your trig function (2 points). How to find the answer (2 points).

Answer 1

1) The diagram is a right triangle, where the base is represented by a segment of unknown length, the height is a segment of 3 units (the hieght of the ramp), and the hypotenuse is a segment of 12 units (the length of the board).

In the diagram, the angle searched is opposed to the height.

2) The trigonometric function that relates the opposed leg and the hypotenuse is the sine function.

sine (angle) = opposed leg / hypotenuse = 3 / 12

3) The answer is found by doing the arc sine function

sine (angle) = 3/12 = 0.25 => angle = arcsine(0.25) = 14.5°.