A road is inclined at an angle of 9 degrees with the horizontal. After driving 10,000 feet along this road, find the driver's increase in altitude?

10,000 * sin(9) = ___ feet

1564.34

To find the driver's increase in altitude, we need to use trigonometry. We can use the sine function to relate the angle of inclination and the increase in altitude. The formula is as follows:

sin(angle) = increase in altitude / distance

Given that the angle of inclination is 9 degrees and the distance driven is 10,000 feet, we can rearrange the formula to solve for the increase in altitude:

increase in altitude = sin(angle) * distance

Plugging in the values, we have:

increase in altitude = sin(9 degrees) * 10,000 feet

Now, the sine function requires the angle to be in radians, so we need to convert 9 degrees to radians by multiplying it by π/180:

increase in altitude = sin(9 degrees * π/180) * 10,000 feet

Calculating the expression:

increase in altitude ≈ sin(0.1571 rad) * 10,000 feet

Using a calculator, we find that sin(0.1571) ≈ 0.1564:

increase in altitude ≈ 0.1564 * 10,000 feet

Finally, we can calculate the result:

increase in altitude ≈ 1,564 feet

Therefore, the driver's increase in altitude is approximately 1,564 feet.