Printable practice: Finding missing sides with sin, cos, tan

📚 Topic Summary

Trigonometry is all about the relationships between the angles and sides of right triangles. The three primary trigonometric ratios – sine (sin), cosine (cos), and tangent (tan) – allow us to find missing side lengths in these triangles when we know an angle and one side. Remember SOH CAH TOA: Sin = Opposite / Hypotenuse, Cos = Adjacent / Hypotenuse, Tan = Opposite / Adjacent. Let's practice applying these ratios!

When solving for missing sides, set up the equation using the appropriate trig ratio based on the given angle and sides. Then, use algebraic manipulation to isolate the unknown side length. Practice is key to mastering these calculations!

🧮 Part A: Vocabulary

Match each term with its correct definition:

1. Term: Opposite
2. Term: Adjacent
3. Term: Hypotenuse
4. Term: Sine
5. Term: Tangent

1. Definition: The side next to the angle (not the hypotenuse).
2. Definition: The ratio of the opposite side to the adjacent side.
3. Definition: The side across from the right angle.
4. Definition: The side across from the angle.
5. Definition: The ratio of the opposite side to the hypotenuse.

📝 Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

In a right triangle, the ______ is the longest side. The sine of an angle is the ratio of the ______ side to the hypotenuse. The cosine of an angle is the ratio of the adjacent side to the ______. The tangent of an angle is the ratio of the opposite side to the ______ side.

🤔 Part C: Critical Thinking

Explain in your own words how you choose which trigonometric ratio (sin, cos, or tan) to use when solving for a missing side in a right triangle.