Question

a car is travelling up a slope. the car travels 20km and the road forms an angle of 55° to the horizontal. how much further horizontally is the car from the point at which it started?

Explanation:

Step1: Recall the cosine formula

In a right - triangle, if the hypotenuse is \(c\) and the adjacent side to an angle \(\theta\) is \(a\), then \(\cos\theta=\frac{a}{c}\). Here, \(c = 20\mathrm{km}\) and \(\theta = 55^{\circ}\), and we want to find the adjacent side \(a\) (horizontal distance).

Step2: Calculate the horizontal distance

We know that \(a = c\times\cos\theta\). Substitute \(c = 20\) and \(\theta=55^{\circ}\) into the formula. Using a scientific calculator, \(\cos(55^{\circ})\approx0.5736\). Then \(a = 20\times\cos(55^{\circ})\approx20\times0.5736 = 11.472\approx11.47\mathrm{km}\)

Answer:

\(11.47\mathrm{km}\)