Done by: Chew Tian Le (2i302) Lee Liak Ghee (2i310) Low Wei Yang (2i313)- Leader Ng Shen Han (2i316) Agenda Introduction to trigonometry- Right-angled triangles, theta, etc. Trigonometric functions Angle of elevation Angle of depression Applicability in real life Simple problems involving angles of elevation/depression Introduction to Trigonometry Formed from Greek words 'trigonon' (triangle) and 'metron' (measure). Trigonometric triangles are always rightangled triangles More on Trigonometry A branch of mathematics that studies • Triangles • Relationship between sides and angles between sides Uses • Describes relationship trigonometric between sides/angles functions Sides of a Right-angled Triangle Hypotenuse • Opposite to the right-angle • Longest side Adjacent • Side that touches θ Opposite • Side opposite to θ Theta 8th letter of the Greek alphabet Represented by “θ” A variable, not a constant Commonly used in trigonometry to represent angle values Trigonometric Functions Sin (Sine)= ratio of opposite side to the hypotenuse Cos (Cosine)= ratio of adjacent side to the hypotenuse Tan (Tangent)= ratio of opposite side to the adjacent side Easier way to remember Sin, Tan, Cos TOA CAH SOH (Big foot auntie in Hokkien) TOA: Tangent = Opposite ÷ Adjacent (T=O/A) CAH: Cosine = Adjacent ÷ Hypotenuse (C=A/H) SOH: Sine = Opposite ÷ Hypotenuse (S=O/H) Trigonometric Functions Angle of Elevation The angle of elevation is the angle between the horizontal line and the observer’s line of sight, where the object is above the observer Angle of Depression The angle of depression is the angle between the horizontal line and the observer’s line of sight, where the object is below the observer Applicability of Angles of Elevation and Depression Used by architects to design buildings by setting dimensions Used by astronomers for locating apparent positions of celestial objects Used in computer graphics by designing 3D effects properly Used in nautical navigations by sailors (sextants) Many other uses in our daily lives Simple Word Problem involving Angles of Elevation Little Tom, who is 0.75 metres tall is looking at a bug on the top of a big wall, which is 11 times his height. He is standing 2 metres away from the wall. What angle is he looking up at? Solution: Actual height of ceiling: 0.75m x (11)= 8.25m Subtract off his own body height: 8.25m - 0.75m = 7.5m tan(θ) = 7.5m ÷ 2m tan-1(7.5 ÷ 2) = 75.1... o Simple Word Problem involving Angles of Depression A boy 1m tall is standing on top of a staircase 33m high while looking at a patch of grass on the ground 50m away from him. Find the angle from which he is looking at. Solution: • Actual height boy is looking from: 33m + 1m = 34m • sin(θ) = 34m ÷ 50m • sin-1(34 ÷ 50) = 42.8...o Overall summary • • • • Draw the diagram Identify the known values Form equations Solve We hope you have enjoyed our presentation Thank you for your kind attention! Please ask reasonable questions, if any.