# Two vectors from an angle of 110°. One of the vectors is 20 units long and makes an angle of 40° with the vector sum of the two. Find the magnitude of the second vector and of the vector sum?

Jan 15, 2018

13.71 units

#### Explanation:

If the sum of two vector $a$ and $b$ is $C$ and that angle between $a$ and $b$ is $\theta$ and that of $a$ and $C$ is $\alpha$ then the relation is given as,

$\tan \alpha$ = $\frac{b \sin \theta}{a + b \cos \theta}$

Here, $\alpha$ = 40 degrees
$b$ is unknown,$\theta$ = 110 degrees and $a$ is 20 units

Putting all the values we get, $b$ is 13.71 units

derivation of the formula is given below