Question

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.

Answer 1

sin 10° =
x
4000

4000 sin 10° = x
x ≈ 695 ft

Answer 2

got it:) lol

Answer 3

Perfect close-approximation answer above.

Eyeball estimation method, when you have no calculator:
For small angles, at a distance of 60, the number of degrees and the distance are about the same. So, in this case, at 60, the distance will be 10. At 600, the distance will be 100. At 4000, the distance will be estimated to be about 20/3 the distance at 600, or 667. You can see it's off by a little, but a five percent error without a calculator isn't too bad in real life.

In a math class, it is probably only good to check your work.