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?
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.
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
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.
To find the change in the truck's altitude, you need to calculate the vertical distance covered by the truck along the inclined road.
First, let's break down the problem:
1. The road is inclined at a 3° angle.
2. The truck travels 10,000 feet on the road.
To calculate the change in altitude, we can use trigonometry. The sine function relates the angle of inclination to the ratio of the change in altitude and the distance covered along the inclined road.
The formula for calculating the change in altitude is:
Change in altitude = Distance traveled × sin(angle of inclination)
Now let's solve the problem using this formula:
Change in altitude = 10,000 feet × sin(3°)
To find the value of sin(3°), you can use a scientific calculator or an online trigonometric calculator.
Plug in the values and calculate:
Change in altitude = 10,000 feet × 0.05234
Change in altitude ≈ 523.4 feet
Therefore, the change in the truck's altitude would be approximately 523.4 feet along the inclined road.