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© Boardworks Ltd of 43 θ OPPOSITEOPPOSITE H Y P O T E N U S E A D J A C E N T The three trigonometric ratios Sin θ = Opposite Hypotenuse S O H Cos θ = Adjacent Hypotenuse C A H Tan θ = Opposite Adjacent T O A Remember: S O H C A H T O A
© Boardworks Ltd of 43 Finding side lengths If we are given one side and one acute angle in a right-angled triangle we can use one of the three trigonometric ratios to find the lengths of other sides. For example, 56° x 12 cm Find x to 2 decimal places. We are given the hypotenuse and we want to find the length of the side opposite the angle, so we use: sin θ = opposite hypotenuse sin 56° = x 12 x = 12 × sin 56° = 9.95 cm
© Boardworks Ltd of 43 Finding side lengths A 5 m ladder is resting against a wall. It makes an angle of 70° with the ground. 5 m 70° x What is the distance between the base of the ladder and the wall? We are given the hypotenuse and we want to find the length of the side adjacent to the angle, so we use: cos θ = adjacent hypotenuse cos 70° = x 5 x = 5 × cos 70° = 1.71 m (to 2 d.p.)
© Boardworks Ltd of 43 Finding side lengths
© Boardworks Ltd of 43 The inverse of sin sin θ = 0.5, what is the value of θ ? To work this out use the sin –1 key on the calculator. sin –1 0.5 =30° sin –1 is the inverse of sin. It is sometimes called arcsin. 30° 0.5 sin sin –1
© Boardworks Ltd of 43 The inverse of cos Cos θ = 0.5, what is the value of θ ? To work this out use the cos –1 key on the calculator. cos –1 0.5 =60° Cos –1 is the inverse of cos. It is sometimes called arccos. 60° 0.5 cos cos –1
© Boardworks Ltd of 43 The inverse of tan tan θ = 1, what is the value of θ ? To work this out use the tan –1 key on the calculator. tan –1 1 =45° tan –1 is the inverse of tan. It is sometimes called arctan. 45° 1 tan tan –1
© Boardworks Ltd of 43 Finding angles We are given the lengths of the sides opposite and adjacent to the angle, so we use: tan θ = opposite adjacent tan θ = 8 5 = 57.99° (to 2 d.p.) θ 5 cm 8 cm θ = tan –1 (8 ÷ 5) Find θ to 2 decimal places.
© Boardworks Ltd of 43 Finding angles
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© Boardworks Ltd of 43 S3 Trigonometry KS4 Mathematics.
The Right Triangle Right Triangle Pythagorean Theorem Trigonometric Functions Inverse Trig Functions Trigonometric Expressions.
TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S.
In each triangle, find the length of the side marked x. If required, round your answers to 1d.p. 144 cm x 60 cm 13 mm x 5 mm 55 mm x 40 mm 164 cm x 230.
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Trigonometry-6 Finding Angles in Triangles. Trigonometry Find angles using a calculator Examples to find sin, cos and tan ratios of angles Examples to.
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θ hypotenuse adjacent opposite There are 6 trig ratios that can be formed from the acute angle θ. Sine θ= sin θCosecant θ= csc θ Cosine θ= cos θSecant.
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Students will recognize and apply the sine & cosine ratios where applicable. Why? So you can find distances, as seen in EX 39. Mastery is 80% or.
1 What you will learn How to find the value of trigonometric ratios for acute angles of right triangles More vocabulary than you can possibly stand!
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Adjacent = Cos o x H Cosine Ratio To find an adjacent side we need 1 side (hypotenuse) and the included angle. a = Cos ° x H a = Cos 60° x 9 a = 0.5 x.
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