A road has an incline of 10°. To the nearest foot, find the increase in altitude of a car after driving 4,000 feet along the road.
tan 10° = h/4000
take it from there
actually you would use sine for this problem
To find the increase in altitude of a car after driving 4,000 feet along a road with a 10° incline, you can use trigonometry.
The increase in altitude can be found using the formula:
Increase in altitude = distance * sin(angle)
First, convert the angle from degrees to radians. We know that 1 degree is equal to π/180 radians. So, we can calculate:
10° * (π/180) = 0.17453293 radians (rounded to 8 decimal places)
Now, we can plug in the values into the formula:
Increase in altitude = 4,000 feet * sin(0.17453293)
Using a scientific calculator or a calculator with a trigonometric function, we can evaluate sin(0.17453293) to be approximately 0.17364818 (rounded to 8 decimal places).
Therefore,
Increase in altitude ≈ 4,000 feet * 0.17364818
Calculating this expression, we find:
Increase in altitude ≈ 694.59 feet
To the nearest foot, the increase in altitude of the car after driving 4,000 feet along the road with a 10° incline is approximately 695 feet.