# An airplane flies on a course of 110° at a speed of 1200 km/h. How far east of its starting point is it after 2 h?

Apr 1, 2018

$2255.3$ km. ( 1 d.p. )

#### Explanation:

From the diagram.

If the plane starts a point S on a bearing of ${110}^{\circ}$, travelling at 1200 km/h, after 2 hrs it will be at point P.

Distance from S to P:

$2 \times 1200$ km/h = 2400 km.

If we are looking for the distance due east the plane is after 2 hrs, this is marked as X on the diagram.

We can find this distance using the cosine ratio. We first need to find angle a.

$a = {110}^{\circ} - {90}^{\circ} = {20}^{\circ}$:

$\therefore$

$\cos \left(a\right) = \text{adjacent"/"hypotenuse} = \frac{X}{2400}$

$\cos \left({20}^{\circ}\right) = \frac{X}{2400}$

Rearanging:

$X = 2400 \cos \left({20}^{\circ}\right) = 2255.3$ km. ( 1 d.p. )