
	Sequences and Series
	Rational Expressions
	Financial Mathematics
	Quadratic Functions and Complex Numbers
	Trigonometric Functions
	Graphing Trigonometric Functions

Topic

The Sine and Cosine Laws in acute and obtuse triangles.

Team members

Names: Maryam Mohammad Amin

Overview

This section is about Sine and Cosine Laws in acute and obtuse triangles.

Necessary Skills

�

Sine Law

� Cosine Law c² = a² + b² - 2ab�cos A

�

Study Tips, Methods and or Advice

In order to be successful in this chapter you must:

� Practice

� Doing homework

� Making notes

Sample Questions and complete solutions

Questions

Complete Solutions

1.Find all the lengths

Given

BAC= 84
ACB=60
ABC=36
AC=3.9 cm

Use Sine Law

$\frac{a}{sin{A}} = \frac{b}{sin{B}} = \frac{c}{sin{C}}$

a sin 36=3.9 sin 84

a 0,5= 3.8

$c^2 = a^2 + b^2 - 2ab\cos(\gamma) . \;$ Use Cosine Law

c=57,76+15,21-(7.6)(3.9) Cos 60

c=72.97-29.64

c=43.33

c = 6.5

2. Find all the lengths

Given

ABC=45
BCA=55
CAB=80
CA=8.7 cm

� Use Sine Law

$\frac{a}{sin{A}} = \frac{b}{sin{B}} = \frac{c}{sin{C}}$

cSine45=8.7sin 55

c0.707=7.12

C=10

aSin 55=10sin 80

a= 12

3. Given

� ABC

� AC=6.6cm

� AB=7.2cm

� BC=8.4cm

Label all missing angles directly on the diagram below.

$c^2 = a^2 + b^2 - 2ab\cos(\gamma) . \;$

� Use Cosine Law

Cos A=

Cos A= 74

8.4sinB=488

Sin B=58

180-58-74=48

4. ABC, c=5 cm, a=3 cm, and A=30; for each possible ABC,

1. Determine sin C

2. calculate the measure of C to 2 decimal places.

3. Determine the length of the AC to 1 decimal place.

� Solution A Solution B

� Use sin Law

$\frac{a}{sin{A}} = \frac{b}{sin{B}} = \frac{c}{sin{C}}$

C= 56.44

C = 56.44 But from the triangle,

B= 180 � 30 � 56.44 C is obtuse.

B = 93.56 So C=180-56.44

123.56

B=180-30-123.45

B=26.44

Use sin Law

b=5.9

b = 2.6716

Extra Practice Questions and Answers

{Provide 5 extra practice questions with answers only}

Extra Practice Questions	Answers
1. Calculate the length of AC in each triangle C Given AB=4cm BC=5cm ABC=70 A B	AC=5.2
2. Given AB=4cm BC=5cm ABC=110	AC=7.4
3. Given AB=4cm BC=5cm ABC=160	AC=8.9
4.Calculate the length of PQ in each triangle Given QPR=60 PRQ=80 QR=5cm	PQ=5.7
5.Gievn RP=4cm RPQ=110 QRP=40	PQ=5.1

Self Reflection

Personal Reflection � Maryam Mohammad Amin

At the end of this chapter I could investigate other triangles with sides lengths that involve other consecutive integers; such as 2 : 3 : 4 : and 4 : 5 : 6 :

At end of this chapter I learned

� Determine the Sin, Cos, and tangent of angles greater then 90

� Prove identity using the Pythagorean identity

I likes most of all the Sin Law because it was easy and concise. Most of the material was form grade 10. The challenging part for me was when in a triangle

the gave only sides not angles hen we had to Cos A=

Use this formula in order to find Cos A.

This course was the most Practical Math

I have ever had. The in class assignment was

The best idea to study. These were all my

Comments about this wonderful class.