Geometry and Trigonometry Flashcards

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Answer: 10

By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = 10.

The area of a circle with radius 5 is closest to which value? (Use π ≈ 3.14)

Answer: 78.5

Area = πr² = 3.14 × 25 = 78.5.

Two angles of a triangle measure 55° and 75°. What is the measure of the third angle?

Answer: 50°

Sum of angles in a triangle = 180°. Third angle = 180 − 55 − 75 = 50°.

In a right triangle, sin(θ) = 3/5. What is cos(θ)?

Answer: 4/5

sin²(θ) + cos²(θ) = 1. cos²(θ) = 1 − 9/25 = 16/25. cos(θ) = 4/5.

A rectangle has a length of 12 and a width of 7. What is its perimeter?

Answer: 38

Perimeter = 2(l + w) = 2(12 + 7) = 2(19) = 38.

A circle has a circumference of 20π. What is its radius?

Answer: 10

C = 2πr → 20π = 2πr → r = 10.

In a right triangle, the angle opposite the hypotenuse is:

Answer: 90°

By definition, a right triangle contains one 90° angle, and the side opposite to it is the hypotenuse.

What is the volume of a rectangular box with length 4, width 3, and height 5?

Answer: 60

Volume = l × w × h = 4 × 3 × 5 = 60.