Trigonometric Ratios: Finding an Angle

Task goals

• Label the hypotenuse, opposite, and adjacent sides of a right-angled triangle relative to an unknown marked angle, in any orientation.
• Choose the correct ratio (sin, cos, or tan) from the two given sides, using SOH CAH TOA.
• Find a missing angle by substituting the two known sides into the chosen ratio and applying the inverse trigonometric function.
• Round an angle answer to a stated accuracy (1 decimal place unless told otherwise) when the result is not exact.
• Recall exact angle values (0, 30, 45, 60, 90 degrees) from a stated exact trigonometric ratio without a calculator.
• Apply the skill to real-world contexts, including angles of elevation and depression, and to multi-step problems that chain a side-finding step into an angle-finding step.