How to reverse-engineer an angle from two known side lengths
In short: Once you can find the sides of a right-angled triangle, you can also work backward to find the angles. This video demonstrates how to use inverse trigonometric functions to solve for the unknown.
The video explains the process of finding a missing angle in a right-angled triangle when two side lengths are already known. While students often learn to find sides using SOHCAHTOA, this method reverses that logic by isolating the angle.
To find the angle, you substitute the known sides into the appropriate trigonometric ratio: sin(angle) = opposite / hypotenuse, cos(angle) = adjacent / hypotenuse, or tan(angle) = opposite / adjacent. Because the goal is to isolate the angle, you must use inverse functions—written as sin⁻¹, cos⁻¹, or tan⁻¹ on a calculator—to calculate the final value.
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Sources
- Summary by Intellect · source: SOHCAHTOA - Finding Missing Angles | Trigonometry | Maths | FuseSchool
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