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Learning Goal

Part of: Apply trigonometry to general triangles1 of 3 cluster items

Derive triangle area formula

HSG.SRT.D.9

**HSG.SRT.D.9**: (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

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HSG.SRT.D.9: (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

What you'll learn

  1. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary altitude from a vertex perpendicular to the opposite side
  2. Explain why the formula works for acute, right, and obtuse triangles
  3. Apply the formula to find the area of a triangle given two sides and the included angle
  4. Recognize when to use A = (1/2)ab sin(C) versus the base-height formula
  5. Interpret the role of sin(C) geometrically - how the included angle controls area for fixed side lengths
  6. Use the formula to solve real-world problems involving triangular regions

Slides

Interactive presentations perfect for visual learners • 2 slide decks

Slide Video

Watch narrated slides play like a video lesson • Narrated slide playback

Exercises

Practice problems to build fluency and understanding • 1 exercises