# Biophysics Problem 3

A force acts at $\mathrm{30^\circ}$ to the horizontal. Its horizontal component is known to be $\mathrm{300 \;N}$. What are its magnitude and its vertical components?

#### First Step

First make a diagram #### Calculation

Now write the trigonometric relation for the cosine of the $30^\circ$ angle and solve for the magnitude of the force.

Don't forget to consider the units.

Calculation:

$\mathrm{\cos 30 = \frac{adjacent}{hypotenuse} \\ 0.866 = \frac{200\; N}{F} \\ Therefore \; F = 200 \; N /0.866 \\ = 231\; N}$

Note that the answer is incomplete without units ('$N$' for Newtons).

#### Next

Now we have to get the vertical component of $F.$

Use the appropriate trigonometric relation to calculate the magnitude of this component.

You could get this part by using either the sine or tangent of the angle.

$\mathrm{\sin 30 = \frac{opposite}{hypotenuse} \\ 0.5000 = \frac{vertical \; component}{231 \; N} \\ \therefore \; vertical \; component = 0.5000 \times 231 \; N \\ = 116 \; N}$

$\mathrm{\tan 30 = \frac{opposite}{adjacent} \\ 0.577 = \frac{vertical \; component}{200 \; N} \\ \therefore \; vertical \; component \; = 0.577 \times 200 \; N \\ = 116 \; N}$