Question

A road rises 1 m for every 15 m measured along the road. a) What is the angle of inclination of the road to the nearest degree? b) How far does the car travel horizontally when it travels 15 m along the road ? Give the answer to the nearest tenth of a metre.

Answer 1

The answer is below

Explanation:

The road increases by a height of 1 m for every 15 m distance. The slope of a line is the ratio of its rise to run. The slope (m) is the tangent of the inclination. Hence:

Slope = rise / run = tanθ

Where θ is the angle of inclination.

a) Given rise = 1 m, run = 15 m

Slope of road (m) = rise / run

m = 1 m/ 15 m

m = 0.0667

slope = tanθ

tanθ = 0.0667

θ = tan⁻¹(0.0667)

θ = 3.81

θ ≈ 4°

b) cosθ = horizontal distance / 15 m

horizontal distance = 15 m × cos 4

Horizontal distance = 14.96

Horizontal distance = 15 m to nearest tenth