Question 1

What is the formula for the area of a triangle?

Accepted Answer

A = ½ × base × height. The height must be perpendicular to the base. For three known sides, use Heron's formula: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. For two sides and an included angle: A = ½ab·sin(C).

Question 2

How do I find the volume of a cylinder?

Accepted Answer

V = πr²h — multiply the base area (πr²) by the height h. Example: radius = 5 cm, height = 10 cm. V = π × 25 × 10 = 250π ≈ 785.4 cm³. Surface area = 2πr(r+h) ≈ 471.2 cm².

Question 3

What is the Pythagorean theorem?

Accepted Answer

In a right triangle: a² + b² = c², where c is the hypotenuse (longest side). Example: legs 3 and 4 → hypotenuse = √(9+16) = √25 = 5. Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17.

Question 4

When do I use the law of sines vs law of cosines?

Accepted Answer

Law of sines (a/sin A = b/sin B): use for AAS, ASA, or SSA triangles. Law of cosines (c² = a²+b²−2ab·cos C): use for SAS (two sides and included angle) or SSS (three sides). Both can solve any triangle given sufficient information.

Question 5

What is SOH-CAH-TOA?

Accepted Answer

A mnemonic for trig ratios in right triangles. Sin = Opposite/Hypotenuse. Cos = Adjacent/Hypotenuse. Tan = Opposite/Adjacent. Example: angle = 30°, hypotenuse = 10. Opposite = 10·sin(30°) = 5. Adjacent = 10·cos(30°) ≈ 8.66.

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