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Pythagoras' Theorem & Simple Trigonometry
Transcript of Pythagoras' Theorem & Simple Trigonometry
Simple Trigonometry The Pythagorean Theorem
(animation) If given any triangle, if we can prove that the square of the longest side is equal to the sum of the squares of the other two sides of the triangle. Then the angle opposite the longest side is a right angle Pythagoras Theorem The Pythagoras' Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right-angled triangle Conversely In this case if we can prove that then ABC is a right-angled triangle Pythagoras' Theorem Proof Something interesting Example Question Example Question (converse) Basics of Trigonometry
10 min Simple Trigonometric Ratios for Acute Angles Teacher Tips 1 sin, cos, tan are abbrevations for sine, cosine and tangent
Hypotenuse (H) - Side opposite the Right angle, the longest side
Opposite (O) - Side opposite of the angle
Adjacent (A) - Side Adjacent to angle (H) (O) (A) Take a break ! Listen to this song Application of Trigonometric Ratios to Right-angled Triangles Using the Trigonometric ratios to fnd the unknown sides or angles in a right angled triangle Example Teacher's Tips 2 If the Degree of accuracy is not stated and if answer is not exact, answer should be corrected to 3 Significant Figures ( 3 S.F)
This means that intermediate Working anwers must be corrected to 4 S.F
Answers in Degrees should be given correct to 1 Decimal Place (1 D.P)
Check that your Calculator is in 'Degree" mode Trigonometric Ratio
For Obtuse Angles Examples Question Angle of Elevation
Angle of Depression When you look at the airplane, the angle the angle between the line of sight and the horizontal line is call the angle of elevation When you look down at the car, the angle between the horizontal line and the line of sight is called the angle of depression * * Angle of Elevation and Depression with respect to points A & B Are you ready to get
TOA CAH SOH
??? How to find Angles using Trigo Ratios