Mathematics: Geometry and Trigonometry Flashcards

What is the value of tan(30°)?

Answer: 1/√3

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

Two parallel lines are cut by a transversal. If one co-interior (same-side interior) angle is 110°, what is the other co-interior angle?

Answer: 70°

Co-interior angles are supplementary, so the other angle = 180° − 110° = 70°.

A right triangle has hypotenuse 10 and one leg 6. What is the other leg?

Answer: 8

By the Pythagorean theorem, leg = √(10² − 6²) = √(100 − 36) = √64 = 8.

In a right triangle, if cos θ = 3/5, what is sin θ?

Answer: 4/5

Using the Pythagorean identity: sin²θ + cos²θ = 1, so sin θ = √(1 − 9/25) = √(16/25) = 4/5.

What is the sum of interior angles of a hexagon?

Answer: 720°

Sum of interior angles = (n − 2) × 180° = (6 − 2) × 180° = 720°.

A tower stands vertically on level ground. From a point 50 m away, the angle of elevation to the top is 30°. How tall is the tower?

Answer: 50/√3 m

tan(30°) = height/50, so height = 50·tan(30°) = 50/√3 m.

Which transformation maps a shape onto a congruent image without changing its orientation?

Answer: Translation

A translation shifts every point by the same vector, preserving shape, size, and orientation.