# Solving two dimensional vector problems

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**Use the law of sines to solve triangles****Use the law of cosines to solve triangles****Solve a vector word problem using the laws of sines and cosines**

To get to school, Pauline leaves her house and walks due east 1.40 km, then takes a shortcut by walking 0.650 km [35° S of E] through a park. Find her displacement from home to school.

**Solve a difficult vector triangle using geometry**

Solve the equation $\vec{A} + \vec{B} = \vec{C}$.

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###### Topic Notes

In this lesson, we will learn:

- How to solve two dimensional vector problems using the law of sines and the law of cosines

__Notes:__- Often, vector equations in physics problems result in vector triangles which can be solved using trigonometry
- At least three pieces of information are needed to solve a triangle, which can be three side lengths (SSS), two side lengths and one angle (SSA, SAS), or one side length and two angles (SAA, ASA).
- Knowing three angles (AAA) does not let you solve a triangle since you will not be able to solve for the side lengths. There is no way to know the size of the triangle without more information.
- You can always solve a triangle that you know four or more pieces of information about.
- Vector triangles that do not contain right angles can be solved either by
__breaking vectors into their components__or using the__law of sines__and the__law of cosines__, which are trigonometric laws that apply to all triangles

**Law of Sines**

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

a,b,c: length of sides a,b,c

A,B,C: angles opposite sides a, b, c

**Law of Cosines**

$c^2 = a^2 + b^2 - 2ab \,cosC$

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