Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Non-Right Angled Trig - The Law of Sines

What do we know how to find with non-right angled triangles?

Using the area of this triangle...

Proof for the Law of Sines

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

*We can ONLY use this when we have an angle and it's opposite side!

The Law of Sines

*this is in your booklet!

This can be used for right triangles but typically is not!

17.5

50

18.4

12

126

112

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

13.3 km

What happens when we try to use the sine rule?

Doesn't work, we are missing the side opposite the given angle!

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Therefore we need another rule...The Cosine Rule!

There are TWO situations where you use the cosine rule.

1. SAS - two sides and the included angle

2. SSS - all three sides

Find the missing side first!

Then use the Sine Rule.

Find ANY angle first!

Then use the Sine Rule

We can derive the formula using Pythagorean Theorem.(watch the video on the website!)

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

From a triangle using standard labeling,

the cosine rule is:

What important relationship do

you notice?

10.1

33.9

77.1

84.4

75.0

20.6

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Solve the following triangles - EXTRA PRACTICE:

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Law of Sines and Cosines - w/ Answers

IBSL Year 1

February 11, 2016

Homework

Chapter 11.4

11G: 1-4

11I: 1-6