A hill road rises at a steady angle of 30° to the horizontal. A cyclist rides 100 m along this road. The height she gains above her starting level is:

The 100 m is measured along the slope, which is the hypotenuse, so the rise is 100·sin30° = 50 m. Using tan30° instead (100/√3 ≈ 57.7 m) would be right only if the 100 m were the horizontal distance.