Right-Angled Triangle Solutions

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Right-angled triangle with trigonometric ratios

📐 Part 1: Finding Missing Sides

1. In a right-angled triangle, the angle of elevation is 35° and the adjacent side is 12 cm. Find the opposite side. (Use tan 35° = 0.700)

Answer: ________ cm

2. A triangle has a hypotenuse of 15 m and an angle of 42°. Calculate the length of the adjacent side. (Use cos 42° = 0.743)

Answer: ________ m

3. The opposite side is 8.5 cm and the angle is 28°. Find the hypotenuse. (Use sin 28° = 0.469)

Answer: ________ cm

4. Which trigonometric ratio would you use to find the missing side x in each scenario?

a) Given: hypotenuse = 20 cm, angle = 60°, find: opposite side

Sine

Cosine

Tangent

b) Given: adjacent = 15 m, angle = 45°, find: hypotenuse

Sine

Cosine

Tangent

📏 Part 2: Finding Missing Angles

5. In a right-angled triangle, the opposite side is 7 cm and the hypotenuse is 12 cm. Find the angle θ.

Answer: θ = ________°

6. The adjacent side measures 9.2 m and the opposite side measures 6.8 m. Calculate the angle.

Answer: ________° (to 1 decimal place)

7. A ladder of length 5 metres leans against a wall. The bottom of the ladder is 1.8 metres from the base of the wall. What angle does the ladder make with the ground?

Answer: ________° (to the nearest degree)

🏗️ Part 3: Real-World Applications

8. A surveyor stands 25 metres from the base of a building and measures the angle of elevation to the top as 38°. Calculate the height of the building.

Height = ________ metres (to 1 decimal place)

9. A ramp for wheelchair access has a horizontal length of 12 metres and rises 0.8 metres vertically. What angle does the ramp make with the horizontal?

Angle = ________° (to 1 decimal place)

10. From the top of a cliff 45 metres high, the angle of depression to a boat is 25°. How far is the boat from the base of the cliff?

Distance = ________ metres (to the nearest metre)