NBT Mathematics: Geometry and Trigonometry 3 — Questions and Answers
Question 1: What is the value of tan(30°)?
- 1/√3 (Correct answer)
- √3
- 1/2
- √3/2
Correct answer: 1/√3
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?
- 70° (Correct answer)
- 110°
- 80°
- 100°
Correct answer: 70°
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?
- 8 (Correct answer)
- 7
- 4
- √136
Correct answer: 8
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?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 3/5
Correct answer: 4/5
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?
- 720° (Correct answer)
- 540°
- 900°
- 1080°
Correct answer: 720°
Sum of interior angles = (n − 2) × 180° = (6 − 2) × 180° = 720°.
Question 6: 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?
- 50/√3 m (Correct answer)
- 50√3 m
- 25 m
- 100 m
Correct answer: 50/√3 m
tan(30°) = height/50, so height = 50·tan(30°) = 50/√3 m.
Question 7: Which transformation maps a shape onto a congruent image without changing its orientation?
- Translation (Correct answer)
- Reflection
- Rotation by 180°
- Dilation
Correct answer: Translation
A translation shifts every point by the same vector, preserving shape, size, and orientation.
NBT Mathematics: Geometry and Trigonometry 3
What is the value of tan(30°)?