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Identify the names of the sides of these right angled-triangles given angle k

TOPIC : TRIGONOMETRY Aim : To be able to name the sides of a right angled triangle (RAT) given and interior angle. Identify the names of the sides of these right angled-triangles given angle k What can you say about the names of the sides?

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Identify the names of the sides of these right angled-triangles given angle k

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  1. TOPIC: TRIGONOMETRYAim: To be able to name the sides of a right angled triangle (RAT) given and interior angle. • Identify the names of the sides of these right angled-triangles given angle k • What can you say about the names of the sides? • They are named according to the angle under consideration. opposite b opposite a b c c adjacent hypotenuse hypotenuse a k a opposite adjacent k c adjacent hypotenuse b k c opposite hypotenuse b k a adjacent

  2. TOPIC: TRIGOOMETRYAim: To Understand the 3 Trigonometric Ratios • The 3 ratios are Sine, Cosine and Tangent • Using pneumonic, the ratios are SOH, CAH, TOA

  3. Finding the length of an unknown side of a right angled triangle: The appropriate ratio to use is Tangent, i.e. TOA Tan 260 = a/7 a/7 = Tan 260 a = 7 x Tan 260 a = 7 x 0.4877 a =3.41cm (to 2 d.p.) Calculate the length of y. NB: The appropriate ratio is sine, SOH Sine 340 = y/5 y/5 = Sine 340 y = 5 x Sine 340 y = 5 x 0.559 y =2.80m (to 2 d.p.) TOPIC: TRIGONOMETRYAim: To use Trigonometry to find lengths,given an interior angle and one side of a RAT (hypotenuse) 5m y a (opposite) (opposite) 34o 26o 7cm (adjacent)

  4. TOPIC: TRIGONOMETRYQuestions for Students to Attempt. • Calculate the length of y • NB: The appropriate ratio is Sine, i.e. SOH • Sine 420 = y/6.2 • y/6.2 = Sine 420 • y = 6.2 X Sine 420 • y = 6.2 X 0.669 • y =4.19m (to 2 d.p.) • Calculate the length of side x • The appropriate ratio to use is Cosine, i.e. CAH • Cos 670 = x/10.6 • 0.39 = x/10.6 • x =10.6 X 0.39 • x =4.14m (to 2 d.p.) y (Opposite) Hypotenuse 10.6m Hypotenuse 670 6.2m 420 x (Adjacent)

  5. TOPIC: TRIGONOMETRYStarter • Evaluate the following • Tan 50 • Sin 50 • Cos-1 0.56 • Tan-1 40 • Sin-10.50 = 1.19 = 0.76 = 55.94 = 88.85 = 30

  6. To find angle a The appropriate ratio to use is Tangent, i.e. TOA Tan a = 32/25 Tan a = 1.28 a = Tan -1 1.28 a = 52.00 To find the size of angle y TOPIC: TRIGONOMETRYAim: To Find an interior angle of a RAT • NB: The appropriate ratio is • Sine , i.e. SOH • Sine y = 30/50 • Sine y = 0.6 • y = Sine-1 0.6 • y = 36.90, approximately 370 32cm (Opposite) 50cm 25cm (Opposite) Hypotenuse 30cm a Adjacent y0

  7. TOPIC: TRIGONOMETRYQuestions for students to attempt. • Find angle y • NB: The appropriate ratio is Cosine, i.e. CAH • Cos y = 12.4/19.7 • Cos y = 0.639 • y = Cos-1 0.639 • y = 50.280 • y is approximately 500 • Find angle b • The appropriate ratio to use is Sine, i.e. SOH • Sin b = 6/12 • Sin b = 0.5 • b = Sin-1 0.5 • b = 300 (Adjacent) 12.4m Hypotenuse y Opposite 12cm 6cm Hypotenuse b 19.7m

  8. TOPIC: TRIGONOMETRYAim: To Use Trigonometry to Solve Problems • Key words • Angle of Elevation:is an angle between the horizontal and an object above it • Angle of Depression /Descent: is an angle between the horizontal and an object below it • Tips: Draw and label your diagram • Write down the formula to be used and calculate the answer

  9. An aeroplane is 4500m from touchdown. Its angle of descent is 500 to horizontal. How high is it above the ground. The angle of descent is outside the right angled-triangle. So we need to find the angle inside it. TOA is the ratio to use 4500/a = Tan 400 4500/a = 0.8390 a = 4500 / 0.8390 a = 5363.52m TOPIC: TRIGONOMETRYAim: To Use Trigonometry to Solve Problems 500 400 a Runway Ground 4500m Touchdown

  10. TOPIC: TRIGONOMETRYAim: To Use Trigonometry to Solve Problems • The appropriate ratio is SOH • Sin 450 = 50/a • 0.71 = 50/a • a = 50 / 0.71 • a = 70.42km • A boat is due South of a Lighthouse. • It sails on a bearing 0450 until it is due east of the lighthouse. If the boat is now 50km away from the lighthouse, how far has it sailed. 50km (Opposite) East a Hypotenuse 0450 South

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