Medium Level
Geometry
Advance your geometry skills with circles, similar triangles, and trigonometry.
What You'll Learn
Circles
Work with circle equations, arc length, sector area, and inscribed angles.
Similar Triangles
Use properties of similar triangles to find missing side lengths and angles.
Trigonometric Ratios
Apply sine, cosine, and tangent to solve right triangle problems.
Volume & Surface Area
Calculate volume and surface area of cylinders, cones, and spheres.
Key Concepts
- •Circle Equation: (x - h)² + (y - k)² = r² where (h,k) is center and r is radius
- •Similar Triangle Ratios: Corresponding sides are proportional
- •SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
- •Arc Length: s = rθ where θ is in radians
- •Cylinder Volume: V = πr²h
Example Problem
In a right triangle, if the hypotenuse is 10 and one angle is 30°, what is the length of the side opposite the 30° angle?
Solution:
Using sine: sin(30°) = opposite/hypotenuse
sin(30°) = opposite/10
0.5 = opposite/10
opposite = 5
Study Tips
- ✓Memorize special right triangle ratios: 30-60-90 (1:√3:2) and 45-45-90 (1:1:√2)
- ✓When working with circles, identify whether you need circumference, area, or arc length
- ✓Set up proportions carefully when solving similar triangle problems
- ✓Know your calculator: make sure you're in degree mode for most SAT problems
Start Practicing
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