📐 Part 1: Identifying Triangle Parts

1. In a right-angled triangle, label the following parts relative to angle θ:

Draw a right triangle and clearly label: hypotenuse, opposite side, and adjacent side

2. Complete the trigonometric ratio definitions by filling in the blanks:

sin θ = _____________ ÷ _____________

cos θ = _____________ ÷ _____________

tan θ = _____________ ÷ _____________

🔢 Part 2: Applying Trigonometric Ratios

3. A right triangle has a hypotenuse of 10 metres and an angle of 30°. Find the length of the opposite side.

4. In a right triangle, the adjacent side is 8 centimetres and the angle is 45°. Calculate the length of the opposite side.

5. A ladder leans against a wall. The ladder is 5 metres long and makes a 60° angle with the ground. How high up the wall does the ladder reach?

📊 Part 3: Finding Unknown Angles

6. In a right triangle, the opposite side is 6 metres and the hypotenuse is 10 metres. Find the angle θ.

7. A ramp has a horizontal distance of 12 metres and rises 3 metres vertically. What angle does the ramp make with the horizontal?

🏗️ Part 4: Real-World Applications

8. A surveyor stands 50 metres from the base of a building and measures the angle of elevation to the top as 35°. Calculate the height of the building.

9. From the top of a lighthouse that is 40 metres high, the angle of depression to a boat is 25°. How far is the boat from the base of the lighthouse?

10. Which trigonometric ratio would you use in each situation? Circle the correct answer:

a) Finding the height of a tree when you know the distance from the tree and the angle of elevation:

sine

cosine

tangent

b) Finding the angle when you know the opposite side and hypotenuse:

sine

cosine

tangent