Question

a car is travelling up a slope. the car travels 11km and the road forms an angle of 5° to the horizontal. how much further horizontally is the car from the point at which it

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, \(c = 11\mathrm{km}\) and \(\theta = 5^{\circ}\), and we want to find \(a\).

Step2: Calculate the adjacent side

We know that \(a = c\times\cos\theta\). Substitute \(c = 11\) and \(\theta=5^{\circ}\) into the formula. Using a scientific calculator, \(\cos(5^{\circ})\approx0.9962\). Then \(a = 11\times\cos(5^{\circ})\approx11\times0.9962 = 10.9582\approx10.96\mathrm{km}\)

Answer:

\(10.96\mathrm{km}\)