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

Trigo Ratios of Acute angles P Q TOA CAH SOH

Applications – Angle of elevation and Angle of depression

Applications – Angle of elevation and Angle of depression

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

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

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:

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

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

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

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!

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

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°)