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THE SINE RULE Powerpoint hosted on www.worldofteaching.com Please visit for 100’s more free powerpoints

b) two sides and an angle opposite a given side The Sine Rule is used to solve any problems involving triangles when at least either of the following is known: a) two angles and a side b) two sides and an angle opposite a given side                                                                                                                                              In Triangle ABC, we use the convention that a is the side opposite angle A b is the side opposite angle B A c b B C a The sine rules enables us to calculate sides and angles In the some triangles where there is not a right angle.

Solve triangle ABC in which ÐA = 55°, b = 2.4cm and Example 2 (Given two sides and an included angle)     Solve triangle ABC in which ÐA = 55°, b = 2.4cm and c = 2.9cm    By cosine rule, a2 = 2.42 + 2.92 - 2 x 2.9 x 2.4 cos 55°     = 6.1858   a = 2.49cm                                  <>

Using this label of a triangle, the sine rule can be stated Either [1] Or [2] Use [1] when finding a side Use [2] when finding an angle

Example: A Given Angle ABC =600 Angle ACB = 500 c 7cm Find c. B C To find c use the following proportion: c= 6.19 ( 3 S.F)

C SOLUTION: 6 cm 15 cm 1200 A B sin B = 0.346 B= 20.30

DRILL: SOLVE THE FOLLOWING USING THE SINE RULE: Problem 1 (Given two angles and a side) In triangle ABC, ÐA = 59°, ÐB = 39° and a = 6.73cm. Find angle C, sides b and c. Problem 2 (Given two sides and an acute angle) In triangle ABC , ÐA = 55°, b = 16.3cm and a = 14.3cm. Find angle B, angle C and side c.    Problem 3 (Given two sides and an obtuse angle) In triangle ABC ÐA =100°, b = 5cm and a = 7.7cm Find the unknown angles and side. 

Answer Problem 1 ÐC = 180° - (39° + 59°)           = 82°                                 

ANSWER PROBLEM 2 = 0.9337 = 14.5 cm (3 SF)

Answer Problem 3

THE COSINE RULE

Sometimes the sine rule is not enough to help us solve for a non-right angled triangle. For example: C a 14 B 300 18 A In the triangle shown, we do not have enough information to use the sine rule. That is, the sine rule only provided the Following: Where there are too many unknowns.

The cosine Rule: To find the length of a side For this reason we derive another useful result, known as the COSINE RULE. The Cosine Rule maybe used when: Two sides and an included angle are given. Three sides are given C a C A b B a c c A B The cosine Rule: To find the length of a side a2 = b2+ c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B c2 = a2 + b2 - 2ab cos C

THE COSINE RULE: To find an angle when given all three sides.

Example 1 (Given three sides)      In triangle ABC, a = 4cm, b = 5cm and c = 7cm. Find the size of the largest angle. The largest angle is the one facing the longest side, which is angle C.                                                                                                                                                     

DRILL: ANSWER PAGE 203 #’S 1-10

END THANK YOU!!!