NBT Mathematics: Geometry and Trigonometry 3

Question 1

What is the value of tan(30°)?

Accepted Answer

1/√3

Answer

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

Question 2

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?

Accepted Answer

70°

Answer

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

Question 3

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

Accepted Answer

8

Answer

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

Question 4

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

Accepted Answer

4/5

Answer

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

Question 5

What is the sum of interior angles of a hexagon?

Accepted Answer

720°

Answer

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

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