a mass of 5kg is suspended by two strings, 24cm and 32cm long, from two points that are 40cm apart and at the same level. determine the tension in each of the strings.
To get started use the law of cosines
$\displaystyle c^2=a^2+b^2-2ab\cos(\alpha)$
Since you know the length of the three sides of the triangle you can use this to find the angles in the triangle.
Then just break your forces into the x and y component.
I hope this gets you started.
1. Draw a sketch of the triangle ABC. (see attachment). Use the Cosine rule to determine the interior angles of the triangle.
2. Convert the measurement of the mass into the value of the weight (in Newton):
$\displaystyle 5\ kg \cdot 9.81\ \frac m{s^2} = 49.05\ N$
3. The force $\displaystyle \vec F$ has the same magnitude as the force $\displaystyle \vec W$ but is pointing in the opposite direction. The force $\displaystyle \vec F$ is produced by the forces of the two strings. To calculate their magnitude use Sine rule.
4. I've got $\displaystyle | \overrightarrow{F_{CA}} |= 40.01\ N$ and $\displaystyle | \overrightarrow{F_{CB}} |= 22.77\ N$
$\displaystyle \overrightarrow{F_{CA}}$ denotes the force which effects in the direction of CA.