Key formulas for triangles, circles, and basic trig ratios (SOH CAH TOA).
Find the hypotenuse of a right triangle with legs 6 and 8.
Pythagorean theorem: a²+b²=c² → 6²+8²=36+64=100 → c=√100=10.
What is the area of a triangle with base 10 and height 4?
Area = (1/2)*base*height = (1/2)*10*4 = 20.
A circle has diameter 12. What is its circumference?
Circumference = πd = π*12 = 12π. Radius=6 but formula uses diameter.
In a 30-60-90 triangle, if the short leg is 5, what is the hypotenuse?
Ratio: short leg : long leg : hypotenuse = 1 : √3 : 2. Hypotenuse = 2*5 = 10.
If tan(θ) = 3/4, what is sin(θ)?
tan = opposite/adjacent = 3/4. Hypotenuse = √(3²+4²)=5. sin = opposite/hypotenuse = 3/5.
What is the volume of a cylinder with radius 3 and height 7?
Volume = πr²h = π*9*7 = 63π.