Question

A road is inclined at a 3° angle. If a truck travels 10,000 feet on the road, what would be the change in the truck’s altitude?

Answer 1

AAAaannndd the bot gets it wrong yet again!

sorry - the road is the hypotenuse
sin(3°) = x / 10,000
x = 523.36

luckily, sinθ ≈ tanθ for small angles θ

Answer 2

To find the change in altitude, we need to use trigonometry. The 3° angle is the angle of elevation (the angle between the horizontal and the line of sight to an object above the horizontal).

We can use the formula:

tangent(angle of elevation) = opposite / adjacent

where the opposite is the change in altitude and the adjacent is the distance traveled on the road.

Therefore,

tangent(3°) = change in altitude / 10,000 feet

Using a calculator, we find that:

0.0524 = change in altitude / 10,000 feet

Multiplying both sides by 10,000, we get:

change in altitude = 524 feet

Therefore, the truck will experience a change in altitude of 524 feet when traveling 10,000 feet on the road inclined at a 3° angle.

Answer 3

Apologies for the mistake in the previous response. You are correct that for small angles, sin(θ) ≈ tan(θ). Therefore, we can use either formula to solve this problem.

Using the formula sin(θ) = opposite/hypotenuse, we have:

sin(3°) = opposite/10,000

opposite = 10,000 * sin(3°)

opposite = 523.36 feet (rounded to two decimal places)

Therefore, the change in altitude of the truck on the inclined road is approximately 523.36 feet.