Question

A car travels 250 km east and then turns through an angle 25 degrees south of east and travels another 115 km. How far is the car from its starting point? Round to the nearest tenth.

Answer 1

357.5 Km

Step-by-step explanation:

We can model the situation as follows:

Therefore, the car travels through the black lines and we need to find the distance x.

So, first, we will calculate the measure of angle A as follows:

m∠A = 180° - 25° = 155°

Because angle A and the angle that measures 25° form a straight line.

Now, we can use the law of cosine to find the missing sides of the triangle x, so x will be equal to:

`\begin{gathered} x=\sqrt[]{250^2+115^2-2(250)(115)\cos (155)} \\ x=\sqrt[]{62500+13255-(-52112.69)} \\ x=\sqrt[]{62500+13255+52112.69} \\ x=357.5\text{ km} \end{gathered}`

Therefore, the car is 357.5 km far from its starting point.