Basic Trigonometry Questions and Answers

Q: In a right-angled triangle ABC, right-angled at B, AB = 3 cm and BC = 4 cm. Find the value of sin(A) and cos(A).

Solution:

1. First, find the Hypotenuse (AC) using Pythagoras theorem: AC² = AB² + BC² AC² = 3² + 4² = 9 + 16 = 25 AC = 5 cm.
2. For angle A, the Perpendicular (opposite side) is BC (4 cm), the Base (adjacent) is AB (3 cm), and Hypotenuse is AC (5 cm).
3. sin(A) = Perpendicular / Hypotenuse = 4/5
4. cos(A) = Base / Hypotenuse = 3/5

Q: Evaluate: 2 tan² 45° + cos² 30° - sin² 60°

Solution: Using the standard trigonometric table:

• tan 45° = 1
• cos 30° = √3 / 2
• sin 60° = √3 / 2

Put these values into the equation: = 2(1)² + (√3 / 2)² - (√3 / 2)² = 2(1) + (3/4) - (3/4) = 2 + 0 = 2

Q: A ladder is leaning against a wall. The angle of elevation of the ladder to the wall is 60°. If the foot of the ladder is 2.5 meters away from the wall, find the length of the ladder.

Solution: Let the length of the ladder be the hypotenuse (x). The distance from the wall is the Base = 2.5 m. The angle is 60°. We know the Base and want the Hypotenuse, so we use the Cosine ratio.

• cos(60°) = Base / Hypotenuse
• 1/2 = 2.5 / x
• x = 2.5 × 2
• Length of the ladder = 5 meters.