Question

You have been asked to build a ramp for Dan's Daredevil Motorcycle Jump. Base of the ramp is to have width x=140 feet and angle of inclination ?=11 degrees. Find the height y and the length z of the incline. Include units in your answers. All trig functions will be evaluated in degrees.

Height y = ___ (units)

Answer 1

To calculate the height and length of the incline of a ramp with a base width of 140 feet and an angle of inclination of 11 degrees, use the sine function for height (y = 140 feet × sin(11°)) and the cosine function for length (z = 140 feet/cos (11°)).

Step-by-step explanation:

To find the height y and the length z of the ramp's incline for Dan's Daredevil Motorcycle Jump with a base width of x = 140 feet and an angle of inclination θ = 11 degrees, we will use trigonometric functions.

For the height y, we will use the sine function because it relates the opposite side (height) to the hypotenuse (the length of the ramp incline). The formula is y = x × sin(θ).

For the length z of the incline, we will use the cosine function because it relates the adjacent side (base width) to the hypotenuse (the length of the ramp incline). The formula is z = x / cos(θ).

Step by step, first calculate the height (y):

1. Use the sine function with the known angle of 11 degrees: sin(11°).
2. Multiply the result by the base width (x): y = 140 feet × sin(11°).
3. The result is the height y of the ramp in feet.

Next, calculate the length (z):

1. Use the cosine function with the known angle of 11 degrees: cos(11°).
2. Divide the base width (x) by the cosine result: z = 140 feet / cos(11°).
3. The result is the length z of the ramp in feet.

For calculations, remember that trigonometric functions in most calculators require angles to be in degrees.

The exact answers would depend on a scientific calculator to find sin(11°) and cos(11°), but the use of these formulas will give the desired dimensions for Dan's ramp.