- #1

Liquid7800

- 76

- 0

I have two vectors

**a**and

**b**, such that the angle between them is 45 degrees.

The vector

**a+b**and

**a**have an angle between them that is 30.

This produces a problem in 'drawing' a triangle, when trying to solve this problem using the law of sines because the 'triangle' involving vectors

**a**,

**b**, and

**a+b**do not 'add up' to 180 degress because we already have two angles (45 and 30) totalling 75 degrees, thereby needing an angle > 90 within this particular triangle for a sum total of 180 degrees for the triangle (since an individual angle of a triangle can't be more than 90 degrees.

In this case, if the length of |

**a**| = 6

then I have one unknown angle (between

**b**and (

**a+b**) and two unknown magnitudes (|

**b**| and |

**a+b**|)

To therefore 'build' a triangle to solve this problem using the Law of Sines, can I simply 'divide' the angle between

**a**and

**b**or

**a**and

**a+b**to create my triangle, to find |

**b**|?

I appreciate any insight of approaching this problem from the angle of using the Law of Sines (no pun intended), and I hope I discribed my problem clearly enough