Question 1: Calculate the angle in degrees whose sine value is 0.5 using inverse sine (sin⁻¹).

Answer: 30

Question 2: Find the angle in degrees where the cosine ratio is 0.8 using inverse cosine (cos⁻¹).

Answer: 36.87

Question 3: Using inverse tangent (tan⁻¹), determine the angle in degrees if the tangent ratio is 1.

Answer: 45

Question 4: Construct a right-angled triangle where sin(θ) = 0.6. Label all sides and determine the angle θ in degrees.

Answer: θ ≈ 36.87

Question 5: A ladder leans against a wall forming an angle of 45° with the ground. If the ladder is 10 meters long, calculate the height it reaches on the wall using inverse functions.

Answer: ≈ 7.07 meters

Question 6: Determine the angle in degrees when the tangent ratio is 0.5.

Answer: 26.57

Question 7: A tree casts a shadow 15 meters long when the angle of elevation of the sun is 30°. Using inverse functions, find the height of the tree.

Answer: ~8.66 meters

Question 8: Calculate the angle in degrees if the cosine ratio is 0.3.

Answer: 72.54

Question 9: A ramp makes an angle of 60° with the ground. If the ramp is 12 meters long, find the height it reaches using inverse sine.

Answer: ≈ 10.39 meters

Question 10: Identify and correct the mistake: The inverse sine of 1 is 90°, but some students say it's 180°.

Answer: Correct answer: 90°. Mistake: They said 180°, but sin(180°) = 0.

Question 11: Estimate the angle in degrees when the tangent ratio is 2, and explain your reasoning.

Answer: Approximately 63.43°, because tan⁻¹(2) ≈ 63.43°.