a vector has a magnitude of 18.3 cm and a direction of 38 degrees. find the magnitude of its vertical and horizontal components to the nearest tenth.

To find the magnitude of the vertical and horizontal components of a vector, we can use basic trigonometry.

Given:
Magnitude of the vector (hypotenuse) = 18.3 cm
Direction of the vector = 38 degrees

Step 1: Finding the vertical component:
The vertical component of the vector can be found using the sine function (opposite/hypotenuse).

Vertical component = Magnitude * sin(Direction)

Vertical component = 18.3 cm * sin(38 degrees)

Step 2: Finding the horizontal component:
The horizontal component of the vector can be found using the cosine function (adjacent/hypotenuse).

Horizontal component = Magnitude * cos(Direction)

Horizontal component = 18.3 cm * cos(38 degrees)

Now, let's calculate the values:

Vertical component ≈ 11.2 cm (to the nearest tenth)
Horizontal component ≈ 14.5 cm (to the nearest tenth)

Therefore, the magnitude of the vertical component is approximately 11.2 cm and the magnitude of the horizontal component is approximately 14.5 cm.