Trigonometry Ratios Introduction

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Right-angled triangle with trigonometric ratios

📐 Part 1: Triangle Sides and Ratios

1. In a right-angled triangle, which side is always the longest?

Adjacent

Opposite

Hypotenuse

2. Complete the trigonometric ratios:

sin(θ) = _____________ ÷ _____________

cos(θ) = _____________ ÷ _____________

tan(θ) = _____________ ÷ _____________

3. Which trigonometric ratio would you use to find the opposite side when you know the angle and hypotenuse?

Sine

Cosine

Tangent

4. In a right-angled triangle with angle θ = 30°, if the hypotenuse is 10 cm, what is the length of the opposite side? (Use sin(30°) = 0.5)

🔢 Part 2: Problem Solving

5. A ladder leans against a wall at an angle of 60° to the ground. If the ladder is 8 metres long, how high up the wall does it reach? (Use sin(60°) = 0.866)

6. Sarah is standing 15 metres away from the base of a tree. The angle of elevation to the top of the tree is 45°. Calculate the height of the tree. (Use tan(45°) = 1)

7. In a right-angled triangle, the adjacent side is 12 cm and the opposite side is 5 cm. Calculate the angle θ using the tangent ratio.