Trigonometric ratios: sin, cos, and tan

Learning Objectives Identify the hypotenuse, opposite, and adjacent sides of a right-angled triangle with respect to a given acute angle. Define the sine, cosine, and tangent ratios for an acute angle in a right-angled triangle. Calculate the exact values of sin, cos, and tan for a given angle when all three side lengths are known. Use a scientific calculator to find the decimal approximation of sin, cos, and tan for any given angle. Set up a trigonometric equation to find the length of an unknown side in a right-angled triangle. Solve for an unknown side length in a right-angled triangle using the appropriate trigonometric ratio. How can you measure the height of a skyscraper or a giant tree without a massive tape measure? 🌳 Trigonometry gives us the tools to measure the u...

TermDefinitionExample Right-Angled TriangleA triangle that has one angle measuring exactly 90 degrees. The other two angles are always acute (less than 90 degrees).A triangle with angles 30°, 60°, and 90°. HypotenuseThe longest side of a right-angled triangle. It is always the side directly opposite the 90-degree angle.In a triangle with sides 3cm, 4cm, and 5cm, the 5cm side is the hypotenuse. Reference Angle (θ)The specific acute angle in a right-angled triangle that we are focusing on to determine the opposite and adjacent sides.In a triangle ABC with a right angle at C, if we are focusing on angle A, then A is our reference angle. Opposite SideThe side of the triangle that is directly across from the reference angle (θ).If our reference angle is 30°, the side that does not touch this a...

The Sine Ratio (SOH) sin(θ) = \frac{\text{Opposite}}{\text{Hypotenuse}} Use the sine ratio when you know or need to find the Opposite side and the Hypotenuse, relative to a known angle. The Cosine Ratio (CAH) cos(θ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} Use the cosine ratio when you know or need to find the Adjacent side and the Hypotenuse, relative to a known angle. The Tangent Ratio (TOA) tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}} Use the tangent ratio when you know or need to find the Opposite and Adjacent sides, relative to a known angle. Mnemonic: SOH CAH TOA SOH: Sine is Opposite over Hypotenuse. CAH: Cosine is Adjacent over Hypotenuse. TOA: Tangent is Opposite over Adjacent. A memory aid to help you remember the three primary trigonometric...