Trigonometric Ratios (SOH CAH TOA)

SAT Math · Axiom Academy

Trigonometric Ratios (SOH CAH TOA) Master sine, cosine, and tangent to solve real-world and SAT-style trigonometry problems involving right triangles. In this lesson, you'll master: The three basic trigonometric ratios: sine, cosine, tangent The mnemonic "SOH CAH TOA" and how to apply it Finding missing sides in right triangles using trig ratios Finding missing angles using inverse trig functions Common angle values you should memorize Understanding Trigonometric Ratios Trigonometric ratios relate the sides of a right triangle to its angles. For a given angle in a right triangle, we label the sides as: Opposite = the side across from the angle Adjacent = the side next to the angle (not the hypotenuse) Hypotenuse = the longest side (opposite the right angle) The three basic trigonometric ratios are: In a right triangle, the angle is 35°, the adjacent side is 8 cm, and we need to find the opposite side. We know the adjacent side and want the opposite side. Use: A ladder leans against a wall at an angle of 65° from the ground. The ladder is 10 meters long. How high does it reach on the wall? The ladder is the hypotenuse (10 m). The height on the wall is opposite the 65° angle. We're looking for the opposite side. To find an angle when you know the sides, use inverse trigonometric functions: , , and . In a right triangle, the opposite side is 6 and the hypotenuse is 10. Find the angle. We have opposite and hypotenuse, so use sine:

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