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FPC Math 10 Old Trigonometry Provincial Exam. Name:____Key_____ 1) Find the length of DB in centimetres. Answer to two decimal places. Do you see 2 right triangles with the common side BD, let it be x. The top right Δ has an angle of 43° with an opp side a, and an adj side of x. a tan 43° = , x · tan 43° = a x The bottom right Δ has an angle of 15° with an opp side b, and an adj side of x. tan 15° = b , x · tan 15° = b x , ________ ________ Since a + b = 85 cm, so x · tan 43° + x · tan 15° = 85 x · ( tan 43° + tan 15°) = 85 x = 85 = 70.81 cm (tan 43 tan 15) 2) What is the exact value of the length of side x, in centimetres? Do you see 2 right triangles with the common side labeled as y. Notice all the angles in the diagram are special angles, ie: 30°, 60°. Remember special angles have the following properties. Look at the blue right triangle: 5 5 5 cos 60° = , y= = 1 y cos 60 2 1 cos 60° = 2 tan 60° = 3 = 1 3 y = 10 cm Look at the red right triangle: y 10 10 tan 60° = , x= = cm x tan 60 3 FPC Math 10 Old Trigonometry Provincial Exam. Name:________________ 1) Find the length of DB in centimetres. Answer to two decimal places. 2) What is the exact value of the length of side x, in centimetres?