Question

TRIGONOMETRY Adding vectors algebraically find the magnitude of the cars resultant vector?

Answer 1

A car travels 10 km southeast.

The illustration will be :

The angle to the vertical line of southeast is 45 degrees.

Next is 15 km in a direction 60 degrees north of east.

Updating the illustration above.

From the vertical line, the angle is 60 degrees.

The resultant vector is a straight line at starting point to the final point.

And we will form a triangle :

Note that the red marked angle is congruent to 45 degrees.

So the total angle of the vertex is 45 + 60 = 105.

Now using cosine law in finding the third side of a triangle :

`c^2=a^2+b^2-2ab\cos C`

where c = third side

a and b = other two sides

C = angle opposite to the third side.

So we have :

a = 10, b = 15 and angle C = 105 degrees.

Substitute the given values :

`\begin{gathered} c^2=10^2+15^2-2(10)(15)\cos 105 \\ c^2=402.64571 \\ c=\sqrt[]{402.64571} \\ c=20.1 \end{gathered}`

ANSWER :

20.1 km