Area of a Triangle A B 12cm C 10cm Example 1 : Find the area of the triangle ABC. 50 o (i)Draw in a line from B to AC (ii)Calculate height BD D (iii)Area 7.66cm

Area of a Triangle Q P 20cm R 12cm Example 2 : Find the area of the triangle PQR. 40 o (i)Draw in a line from P to QR (ii)Calculate height PS S (iii)Area 7.71cm

Learning Intention Success Criteria 1.Know the formula for the area of any triangle. 1. To explain how to use the Area formula for ANY triangle. Area of ANY Triangle 2.Use formula to find area of any triangle given two length and angle in between.

General Formula for Area of ANY Triangle Consider the triangle below: AoAo BoBo CoCo a b c h Area = ½ x base x height What does the sine of A o equal Change the subject to h. h = b sinA o Substitute into the area formula

Area of ANY Triangle A B C A a B b C c The area of ANY triangle can be found by the following formula. Another version Another version Key feature To find the area you need to knowing 2 sides and the angle in between (SAS)

Area of ANY Triangle A B C A 20cm B 25cm C c Example : Find the area of the triangle. The version we use is 30 o

Area of ANY Triangle D E F 10cm 8cm Example : Find the area of the triangle. The version we use is 60 o

What Goes In The Box ? Calculate the areas of the triangles below: (1) 23 o 15cm 12.6cm (2) 71 o 5.7m 6.2m A =36.9cm 2 A =16.7m 2 Key feature Remember (SAS)

Learning Intention Success Criteria 1.Know how to use the sine rule to solve REAL LIFE problems involving lengths. 1. To show how to use the sine rule to solve REAL LIFE problems involving finding the length of a side of a triangle. Sine Rule

C B A a b c The Sine Rule can be used with ANY triangle as long as we have been given enough information. Works for any Triangle

Deriving the rule B C A b c a Consider a general triangle ABC. The Sine Rule Draw CP perpendicular to BA P This can be extended to or equivalently

Calculating Sides Using The Sine Rule 10m 34 o 41 o a Match up corresponding sides and angles: Rearrange and solve for a. Example 1 : Find the length of a in this triangle. A B C

Calculating Sides Using The Sine Rule 10m 133 o 37 o d = 12.14m Match up corresponding sides and angles: Rearrange and solve for d. Example 2 : Find the length of d in this triangle. C D E

What goes in the Box ? Find the unknown side in each of the triangles below: (1) 12cm 72 o 32 o a (2) 93 o b 47 o 16mm a = 6.7cm b = 21.8mm

Learning Intention Success Criteria 1.Know how to use the sine rule to solve problems involving angles. 1. To show how to use the sine rule to solve problems involving finding an angle of a triangle. Sine Rule

Calculating Angles Using The Sine Rule Example 1 : Find the angle A o A 45m 23 o 38m Match up corresponding sides and angles: Rearrange and solve for sin A o = Use sin to find A o B C

Calculating Angles Using The Sine Rule 143 o 75m 38m X = Example 2 : Find the angle X o Match up corresponding sides and angles: Rearrange and solve for sin X o Use sin to find X o Y Z

What Goes In The Box ? Calculate the unknown angle in the following: (1) 14.5m 8.9m AoAo 100 o (2) 14.7cm BoBo 14 o 12.9cm A o = 37.2 o B o = 16 o