Study guides › Level 9 · Trigonometry

Finding a side with sin, cos or tan

Level 9 · Trigonometry · for questions like “A right triangle has a 20 cm hypotenuse and a 30° angle. How long is the side opposite the 30° angle?”

💡 The idea

Rearrange SOH-CAH-TOA to find a side:

• opposite = hypotenuse × sin
• adjacent = hypotenuse × cos
• opposite = adjacent × tan

✏️ Worked examples

1. Hypotenuse 20, 30°, opposite? 20 × 1/2 = 10.

2. sin A = 3/5 and hypotenuse 25, opposite? 25 × 3/5 = 15.

3. tan A = 3/4 and adjacent 16, opposite? 16 × 3/4 = 12.

⚠️ Watch out

• Name the sides from the angle first.

🎯 Try these

1. Hypotenuse 30, 60° angle. The side next to it?
2. sin A = 5/13, hypotenuse 26. Opposite?
3. tan A = 8/15, adjacent 45. Opposite?

Answers: 1) 15 2) 10 3) 24

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