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Finding the Area of an Oblique Triangle (as in NOT RIGHT)

Finding the Area of an Oblique Triangle (as in NOT RIGHT) 9.2 in text: Find the Area of a Triangle Given Two Sides and An Included Angle (SAS) Extension: Find the Area of a Triangle Given Three Sides and No Angles (SSS). Refresher: What is the area of any triangle?.

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Finding the Area of an Oblique Triangle (as in NOT RIGHT)

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  1. Finding the Area of an Oblique Triangle (as in NOT RIGHT) • 9.2 in text: Find the Area of a Triangle Given Two Sides and An Included Angle (SAS) • Extension: Find the Area of a Triangle Given Three Sides and No Angles (SSS)

  2. Refresher: What is the area of any triangle? But what if you do NOT know the height and all you have are two sides and an included angle? Let’s see what we can derive! Suppose we know sides b and c and their included angle A. What do you know about h in terms of any of the three givens?

  3. Example 1: Find the area of a triangle whose sides have lengths 17 and 16, with included angle 157. Round to nearest hundredth. 53.14 Example 2 (backwards): The area of a triangle is 75 ft2 and two of its sides have lengths 16 ft and 20 ft. Find the measure of the angle, to the nearest degree, included by these two sides. ALERT! There are two answers! Remember, All Students Take Calculus (let’s stick to this version please)? Sin is positive in both quadrants I and II and your calculator will always give you the quadrant I answer. YOU need to remember to calculate the second answer.

  4. Example 3 (overkill): Find the area of an isosceles triangle whose equal sides have length 235 and whose equal angles measure 22. Round to nearest hundredth.

  5. But what if you only know the three sides and NOTHING else? You will now watch a snazzy short video lesson on Heron’s Formula. https://www.khanacademy.org/math/geometry/basic-geometry/heron_formula_tutorial/v/heron-s-formula DO NOW and finish for homework: Trigonometric Relationships Packet (DO NOT LOSE THIS), #1-5, 33-36. Round ALL answers to nearest hundredth. Do you have extra time? Here is a preview of the next lesson. This video is not so great, but she sings much better than me! http://www.youtube.com/watch?feature=player_detailpage&v=o7BkRQw02hQ

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