# Solving two dimensional vector problems

##### Intros

###### Lessons

##### 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 $\vec{A} + \vec{B} = \vec{C}$.

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### 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**

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

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today