What you’ll learn
Find missing angle using inverse trig.
Key idea
Inverse sine converts a side ratio to an angle; use degree mode and round only the final requested angle.
A side ratio is dimensionless, not an angle; round only the final requested angle.
Worked example
Enter the exact value or ordered values in the format requested below.
A right triangle has opposite=36 and hypotenuse=39 relative to acute theta. Use inverse sine to find theta in degrees, rounded to one decimal place.
- sin(theta)=36/39=12/13, so theta=arcsin(12/13) in degrees.
- Theta rounds to 67.4 degrees; its complement rounds to 22.6 degrees, using unrounded theta.
Answer: 67.4
Quick Check
Evaluate a worked attempt at find missing angle using inverse trig, identify the first invalid step, and provide the correction.
A right triangle has opposite=21 and hypotenuse=29 relative to acute theta. Student Step 1 sets theta=arcsin(21/29). Step 2 reports theta=21/29 degrees by treating the ratio as the angle. Locate and repair the first invalid step, rounding the angle to one decimal place.