If the vector v has magnitude 9 and direction 124° (relative to the positive x-axis), what is the component form ⟨x, y⟩ of the vector? Round your answer to the nearest hundredth.

Step-by-step explanation:

The key to solve this exercice is to represent this vector

If you do you will get a rigth triangle (picture below)

The two khown angles of this right triangle are 90° and (180-124)° => 56°

This right triangle has 3 sides where the hypotenus is the magnitude.

The magnitude is the length of the vector.

The other two sides are respectively x and y (the rise and the run)

● sin 56° = opposite / hypotenus

● sin 56° = y / 9

● y = sin 56° × 9

● y = 7.46

● cos 56° = adjacent / hypotenus

● cos 56° = x / 9

● x = cos 56° × 9

● x = 5.03

Let's verify

The pythagorian theorem:

● x^2 + y^2 = 5.03^2 + 7.46^2 = 80.95

80.95 is approximatively 81 wich is 9^2

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The coordinates of the vector are :

(-5.03,7.46)

We have put -5.03 since the direction is 124° wich is in the negative side.

the five is the numerator