you are driving up a long, inclined road. After 1.2 miles you notice that signs along the roadside indicate that your elevation has increased by 530ft. a. What is the angle of the road above the horizontal? b . How far do you have to drive to gain an additional 150ft of elevation ?

Question

you are driving up a long, inclined road. After 1.2 miles you notice that signs along the roadside indicate that your elevation has increased by 530ft. a. What is the angle of the road above the horizontal? b . How far do you have to drive to gain an additional 150ft of elevation ?

Answer 1

can you give me the final answer

Answer 2

To find the angle of the road above the horizontal, you can use trigonometry. The tangent of the angle is equal to the change in elevation divided by the horizontal distance traveled.

a. Let's use the given information to find the angle:

Elevation gained = 530 ft
Distance traveled horizontally = 1.2 miles = 1.2 * 5280 ft (since 1 mile = 5280 ft)

Tangent(angle) = Elevation gained / Distance traveled horizontally

Tangent(angle) = 530 ft / (1.2 * 5280 ft)

Using a scientific calculator or trigonometric table, we can find the inverse tangent (arctan) of (530 / (1.2 * 5280)) to find the angle:

Angle = arctan(530 / (1.2 * 5280))

b. To determine how far you have to drive to gain an additional 150 ft of elevation, we can set up a similar equation:

Additional elevation gained = 150 ft

Let's call the distance you have to drive as "x." Using the same principle as in part (a), we can set up the equation:

Tangent(angle) = Additional elevation gained / Distance to be driven

Tangent(angle) = 150 ft / x

Using the angle calculated in part (a), we can now solve for x:

x = 150 ft / Tangent(angle)

Simply substitute the value for the previously calculated angle into this equation to find the answer.

Answer 3

To find the angle of the road above the horizontal, we can use trigonometry. The angle can be calculated using the inverse tangent function.

Let's start by finding the angle of the inclined road above the horizontal.

a. To calculate the angle, we can use the formula:

angle = arctan(opposite/adjacent)

Here, the opposite side is the change in elevation, which is 530ft, and the adjacent side is the distance traveled, which is 1.2 miles.

First, we need to convert 1.2 miles to feet. Since 1 mile is equal to 5,280 feet, we have:

1.2 miles = 1.2 * 5,280 feet = 6,336 feet

Now, we can substitute these values into the formula:

angle = arctan(530ft / 6,336ft)

Using a calculator, we can find that the angle is approximately 4.77 degrees.

Therefore, the angle of the road above the horizontal is approximately 4.77 degrees.

b. To determine how far you have to drive to gain an additional 150ft of elevation, we need to use the same concept.

Using the formula:

angle = arctan(opposite/adjacent)

The opposite side is now the additional change in the elevation, which is 150ft, and the angle remains the same.

To find the distance, we can rearrange the formula as follows:

adjacent = opposite / tan(angle)

Substituting the values:

adjacent = 150ft / tan(4.77 degrees)

Using a calculator, we can find that the distance you have to drive to gain an additional 150ft of elevation is approximately 1,635.7 feet.

Therefore, you have to drive approximately 1,635.7 feet to gain an additional 150ft of elevation.