Question

Look at the vector below. It is at a 58 degree angle and has a magnitude of 35.

a. What is the length of the x-component of this vector?

b. What is the length of the y-component of this vector?

Answer 1

• x-component: 18.55;
• y-component: 29.68.

Step-by-step explanation

Consider the vector as the hypotenuse of a right triangle. Refer to the diagram attached. The x and y components are the two legs.

The x-component is adjacent to the 58° angle.

`x\text{-component} = \text{Hypotenuse} \cdot \cos{\text{Angle} = 35 * \cos(58\textdegree{}}) = 18.55`.

The y-component is opposite to the 58° angle.

`y\text{-component} = \text{Hypotenuse} \cdot \sin{\text{Angle} = 35 * \sin(58\textdegree{}}) = 29.68`.