Find Area of a Segment in a Circle (3 Methods)

Описание: Learn three different techniques to find the area of a segment in a circle! Mario's Math Tutoring breaks down this challenging geometry concept by first finding the area of the sector (like a pie slice) and then subtracting the area of the inscribed triangle. We'll explore examples with 90°, 60°, and 30° central angles, demonstrating methods like proportions, the 1/2 * a * b * sin(C) triangle area formula, and using special right triangles (30-60-90) and trigonometry (SOH CAH TOA) to find triangle dimensions.

In this video, you'll discover:

0:00 Introduction to Area of a Segment in a Circle
0:20 Understanding a Segment (Sector Area - Triangle Area)
0:50 Example 1: 90° Central Angle, Radius 4cm
1:00 Finding Area of the Sector (Fraction of Circle Area)
2:00 Finding Area of the Right Triangle (1/2 * base * height)
2:40 Calculating Segment Area (4π - 8 cm²)
3:00 Example 2: 60° Central Angle, Radius 10 inches
3:20 Finding Area of the Sector (Using a Proportion)
4:30 Methods for Finding Triangle Area (1/2 * ab * sin(C) or dropping an altitude)
5:00 Using 30-60-90 Special Right Triangles to find triangle base and height
6:00 Calculating Triangle Area
6:30 Calculating Segment Area (50π/3 - 25√3 inches²)
7:40 Example 3: 30° Central Angle, Radius 8 yards
8:00 Finding Area of the Sector (Fraction of Circle Area)
9:00 Method 1 for Triangle Area: 1/2 * ab * sin(C)
9:50 Calculating Segment Area (16π/3 - 16 yards²)
10:10 Method 2 for Triangle Area: Dropping an Altitude and using SOH CAH TOA
11:50 Verifying Triangle Area with Method 2
Master the area of a segment and confidently tackle complex circle geometry problems!

#AreaOfSegment #CircleGeometry #SectorArea #TriangleArea #Geometry #MathTutorial #MathHelp
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