Question 1

A ladder of length 10 m is leaning against a wall. If the ladder makes an angle of 30° with the ground, what is the height of the point on the wall where the ladder touches?

Accepted Answer

Step 1: We use sin(angle) = opposite/hypotenuse. Step 2: sin(30°) = height/10. Step 3: height = 10 × sin(30°) = 10 × (1/2) = 5 m. Therefore, the height is 5 m.

Question 2

If tan(θ) = cot(30°), and 0° < θ < 90°, find the value of θ.

Accepted Answer

Step 1: We are given tan(θ) = cot(30°). Step 2: Using complementary angle identity, cot(30°) = tan(90° − 30°) = tan(60°). Step 3: So tan(θ) = tan(60°), which gives θ = 60°. Therefore, the answer is 60°.

Question 3

If sin(3θ + 15°) = cos(2θ + 25°), where both angles are acute, find the value of θ.

Accepted Answer

Step 1: Use the complementary angle property: sin(A) = cos(B) when A + B = 90°.

Step 2: Set up the equation: (3θ + 15°) + (2θ + 25°) = 90°

Step 3: Simplify: 5θ + 40° = 90°

Step 4: Solve for θ: 5θ = 50°

Step 5: Therefore, θ = 10°

Verification: sin(3×10° + 15°) = sin(45°) = √2/2, and cos(2×10° + 25°) = cos(45°) = √2/2 ✓

SSC CHSL Trigonometry Questions

SSC CHSL Trigonometry — Past Exam Questions

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