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Exploring Sine Law: Triangles, Angles & Sides | Height Calculation | Application Problems

Learn about the Sine Law in a general triangle, deriving rules through perpendiculars and solving for angles and sides. Explore applications like calculating building height based on elevation angles.

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Exploring Sine Law: Triangles, Angles & Sides | Height Calculation | Application Problems

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  1. Consider a general triangle ABC. C b a P A B c The Sine Law Deriving the rule Draw CP perpendicular to BA This can be extended to or equivalently

  2. 2. 1. Not to scale 63o 12.7cm 5.1 cm a 60o 85o 45o m 3. p 15o 145o 45 m The Sine Law To find an unknown side we need 2 angles and a side.

  3. 2. Not to scale 63o 63o 1. 12.7cm 5.1 cm 4.2 cm y y 60o x 11.4cm 3. z 99.7 m 145o 45 m The Sine Law To find an unknown angle we need 2 sides and an angle not included.

  4. The Sine Law The angle of elevation of the top of a building measured from point A is 25o. At point D which is 15m closer to the building, the angle of elevation is 35o Calculate the height of the building. Application Problems T 15 m 145o 35o 25o A B D 10o 36.5 Angle TDA = 180 – 35 = 145o Angle DTA = 180 – 170 = 10o

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