Question

The builder of a parking garage wants to build a ramp at an angle of 10°10° that covers a horizontal span of 7575 feet. how long will the actual ramp be? round your solution to four decimal places.

Answer 1

To calculate the length of the ramp with a 10° angle and a horizontal span of 75 feet, use the formula ramp length = 75 / cos(10°). The length of the ramp, when rounded to four decimal places, is approximately 75.67 feet.

Step-by-step explanation:

The builder of a parking garage wants to calculate the length of a ramp that makes a 10° angle with the ground and spans 75 feet horizontally. To find the actual ramp length, we can use trigonometry, specifically the cosine function. The cosine of an angle in a right triangle is equal to the adjacent side (the ground span) divided by the hypotenuse (the ramp length).

So, cos(10°) = adjacent/hypotenuse, which translates to cos(10°) = 75 / ramp length. We then solve for the ramp length by dividing the horizontal span by the cosine of the angle: ramp length = 75 / cos(10°). Using a calculator, we find that the ramp length is approximately 75.67 feet when rounded to four decimal places.

Here is the step-by-step calculation:

1. Calculate the cosine of the angle: cos(10°).
2. Divide the horizontal span by the cosine of the angle: 75 / cos(10°).
3. Round the result to four decimal places.

Therefore, the actual length of the ramp will be approximately 75.67 feet.

Answer 2

The angle at which builder builds a ramp is 10 degrees

The horizontal span is 75 feet.

When we draw, we get a right angled triangle with its adjacent side as 75 feet and we have to calculate the length of the ramp which is the hypotenuse. Let us assume this to be "x" . Please refer to the attached figure.

Now, we know that the cosine of an angle = adjacent side/hypotenuse side

cos 10 = 75/x

x = 75/cos 10

x = 75/0.984807753

x = 76.1570 Feet

The actual ramp will be 76.1570 Feet