Trigonometric ratios: find a side length

Learning Objectives Identify the hypotenuse, opposite, and adjacent sides of a right-angled triangle relative to a given angle. Recall and apply the SOH CAH TOA mnemonic to select the appropriate trigonometric ratio. Set up a trigonometric equation using sine, cosine, or tangent to represent a problem. Algebraically manipulate a trigonometric equation to solve for an unknown side length. Solve problems where the unknown side is in the numerator of the ratio. Solve problems where the unknown side is in the denominator of the ratio. Use a scientific calculator correctly in degree mode to find solutions. Ever wondered how surveyors measure the width of a river without crossing it? 🏞️ They use the power of trigonometry to measure the unreachable! This tutorial will guide you...

TermDefinitionExample Right-Angled TriangleA triangle containing one angle that measures exactly 90 degrees. The properties of these triangles are the basis of trigonometry.A triangle with angles 30°, 60°, and 90°. HypotenuseThe longest side of a right-angled triangle. It is always the side opposite the 90-degree angle.In a triangle with sides 3, 4, and 5, the side with length 5 is the hypotenuse. Opposite SideThe side directly across from the reference angle (θ) you are working with.If you are considering a 30° angle, the side that does not touch this angle's vertex is the opposite side. Adjacent SideThe side next to the reference angle (θ) that is not the hypotenuse.If you are considering a 30° angle, the adjacent side is one of the two sides that form the angle, but it is not the...

The Sine Ratio (SOH) sin(θ) = \frac{\text{Opposite}}{\text{Hypotenuse}} Use this ratio when you know or need to find the Opposite side and the Hypotenuse, relative to a known angle θ. The Cosine Ratio (CAH) cos(θ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} Use this ratio when you know or need to find the Adjacent side and the Hypotenuse, relative to a known angle θ. The Tangent Ratio (TOA) tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}} Use this ratio when you know or need to find the Opposite and Adjacent sides, relative to a known angle θ.