📚 Topic Summary
Trigonometric ratios (sine, cosine, and tangent) relate the angles of a right triangle to the ratio of its sides. These ratios allow us to find unknown side lengths if we know an angle and one side. The mnemonic SOH CAH TOA is helpful:
- 📐 SOH: Sine = Opposite / Hypotenuse
- 📐 CAH: Cosine = Adjacent / Hypotenuse
- 📐 TOA: Tangent = Opposite / Adjacent
To find a side, identify the known angle, the side you want to find (x), and another known side. Then, decide which trig ratio connects these three elements. Set up the equation and solve for x!
🧮 Part A: Vocabulary
Match the term to its correct definition:
- Hypotenuse
- Opposite
- Adjacent
- Sine
- Tangent
Definitions (Unordered):
- Ratio of the opposite side to the adjacent side.
- Side across from the given angle in a right triangle.
- Ratio of the opposite side to the hypotenuse.
- Side next to the given angle (not the hypotenuse) in a right triangle.
- Longest side of a right triangle, opposite the right angle.
📝 Part B: Fill in the Blanks
Complete the following paragraph using the words: angle, hypotenuse, side, tangent, cosine.
To find a missing ______ of a right triangle using trigonometry, you need to know at least one other ______ and one ______. If you know the adjacent side and the hypotenuse, you would use the ______ ratio. If you know the opposite and adjacent sides, you would use the ______ ratio.
🤔 Part C: Critical Thinking
Explain how you would determine which trigonometric ratio to use when solving for a missing side in a right triangle. Provide an example.