1. Pythagoras Theorem a2 + b2 = c2
where c is the hypotenuse while a and b are the lengths of the other two sides. c a b

2. Trigo Ratios of Acute anglesP Q
TOA CAH SOH

3. Applications – Angle of elevation and Angle of depression

4. Applications – Angle of elevation and Angle of depression

5. A B C a c b h
Proof:
Draw a perpendicular line from A to BC. The length of this line is h, which is the height of the triangle ABC.
Using formula ½ x base x height
Similarly, by drawing perpendicular lines from B to AC and C to AB, we can derive other versions of the formula

6. Sine Rule A B C a c b Divide each term by ½ abc
The ratios of the Sine of an angle to its opposite side are equal

7. Cosine Rule A B C a c b In ∆ABD, using pythagoras theorem:
a - x x
In ∆ABD, using pythagoras theorem:
Similarly, in ∆ADC, using pythagoras theorem:
Using the ratio of cosine in ∆ADC:
Eliminating x and h:

8. Cosine Rule A B C a c b The formula can be rearranged to:
Which one to use depends whether the unknown is a length or an angle

9. Heron’s Formula A B C a c b
where
(1/2 the perimeter of the triangle)

10. Why use Heron’s Formula?B C 9 4 7
Find Area of Triangle ABC.
First:
Find one of the angles, then use formula for Area of triangle

11. Why use Heron’s Formula?B C 9 4 7
Find Area of Triangle ABC.
Using Heron’s Formula:
Advantage:
Answer is more accurate and can be worked out faster!

12. When to use Heron’s Formula?
When ALL 3 sides of the triangle is given/found and you are asked to find AREA

14. Important Points Bearings are measured from the NORTH
Bearings are measured in Clockwise Direction
Bearings are written in 3-digit
(e.g: 030°, 032.1°)