Question

a car is travelling up a slope. the car travels 10km and the road forms an angle of 35° to the horizontal. how much further horizontally is the car from the point at which it started?

Explanation:

Step1: Recall the cosine formula

The cosine of an angle in a right - triangle is given by $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the hypotenuse (distance the car travels along the slope) $c = 10$ km and the angle $\theta=35^{\circ}$, and we want to find the adjacent side (horizontal distance) $a$.

Step2: Substitute values into the formula

We have $a = c\times\cos\theta$. Substituting $c = 10$ and $\theta = 35^{\circ}$, we get $a=10\times\cos(35^{\circ})$.
Using a scientific calculator, $\cos(35^{\circ})\approx0.8192$.

Step3: Calculate the value

$a = 10\times0.8192=8.192\approx8.19$ km.

Answer:

$8.19$ km