Question 1: Calculate the angle of elevation in degrees when the inverse sine of 0.6 is taken.

Answer: 36.87

Question 2: Find the value of θ such that sin⁻¹(0.8) = θ in degrees.

Answer: 53.13

Question 3: Determine the angle given that cos⁻¹(0.5) = θ in degrees.

Answer: 60

Question 4: Calculate the value of θ in degrees where tan⁻¹(1) = θ.

Answer: 45

Question 5: Using inverse sine, find the angle in degrees when sin⁻¹(0.3) is calculated.

Answer: 17.46

Question 6: In architecture, a ramp rises 3 meters over a horizontal distance of 4 meters. Calculate the angle of the ramp in degrees using inverse tangent.

Answer: 36.87

Question 7: A building design requires the roof to be inclined at 25° for aesthetic reasons. If the height of the roof from the base is 5 meters, what is the length of the inclined side? (Use inverse cosine if needed.)

Answer: 10.67

Question 8: Construct a triangle where the angle is 45°, the adjacent side is 5 meters, and find the hypotenuse using inverse cosine.

Answer: 7.07

Question 9: Estimate the value of θ in degrees where tan⁻¹(2) is calculated, and explain the common mistake made when interpreting the inverse tangent value.

Answer: 63.43; Mistake: confusing tan and tan⁻¹, or misreading the calculator answer.

Question 10: A designer uses inverse sine to determine the angle of a support beam, which is 0.75 in ratio form. Calculate this angle in degrees.

Answer: 48.59

Question 11: Identify and correct the mistake in this problem: 'The height of a structure is found by sin⁻¹(0.6). The answer is 60°.'

Answer: Incorrect; sin⁻¹(0.6) ≈ 36.87°, not 60°.