Geometry and Trigonometry Flashcards

An isosceles triangle has two equal sides of length 9 and a base of 6. What is its perimeter?

Answer: 24

Perimeter = 9 + 9 + 6 = 24.

In a right triangle, tan(30°) = ?

Answer: 1/√3

tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.

A right triangle has a hypotenuse of 13 and one leg of 5. What is the other leg?

Answer: 12

a² + 5² = 13² → a² = 169 − 25 = 144 → a = 12.

What is the area of a triangle with base 10 and height 8?

Answer: 40

Area = (1/2) × base × height = (1/2)(10)(8) = 40.

Two supplementary angles are in a ratio of 2:3. What is the measure of the larger angle?

Answer: 108°

Supplementary angles sum to 180°. Larger angle = (3/5) × 180° = 108°.

A cylinder has radius 3 and height 10. What is its volume? (Use π ≈ 3.14)

Answer: 282.6

V = πr²h = 3.14 × 9 × 10 = 282.6.

If cos(θ) = 5/13 in a right triangle, what is sin(θ)?

Answer: 12/13

Using sin²θ + cos²θ = 1: sin²θ = 1 − 25/169 = 144/169, so sinθ = 12/13.

A square has a diagonal of 8√2. What is the side length of the square?

Answer: 8

Diagonal of square = s√2. So s√2 = 8√2 → s = 8.