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Learning Goal
Part of: Apply trigonometry to general triangles — 1 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
- 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
- Explain why the formula works for acute, right, and obtuse triangles
- Apply the formula to find the area of a triangle given two sides and the included angle
- Recognize when to use A = (1/2)ab sin(C) versus the base-height formula
- Interpret the role of sin(C) geometrically - how the included angle controls area for fixed side lengths
- Use the formula to solve real-world problems involving triangular regions
Prerequisites
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