Sample Problem

If the magnitude of a vector is 17, and the angle it makes with the x-axis is 21o, what is its vertical vector component? Round your answer to the nearest hundredth.


SOHCAHTOA tells us that sinθ = opposite ÷ hypotenuse = y-component ÷ vector magnitude.

We know the angle, and the vector. We need to isolate for the y-component.

sin21o = y-component ÷ 17, so the y-component = 17sin21o, and we compute the answer to be approximately 6.09.