Question

TRIGONOMETRY What is the magnitude of the balloons resultant vector?

Answer 1

The directions north and east make a 90° angle, this means that we can make a sketch:

Now, we can see that they form two right triangles, both with legs 18.5 km and 24.6 km and hypotenuse equal to the length of the vector.

This length is the magnitute of the vector, so we can use the Pythagorean Theorem to find the magnitute m:

`\begin{gathered} m^2=(18.5)^2+(24.6)^2 \\ m^2=342.25+605.16 \\ m^2=947.41 \\ m=\sqrt[]{947.41} \\ m=30.7800\ldots\approx30.8 \end{gathered}`

So, the magnitute is approximately 30.8 km.