Pythagoras and Trigonometry Revision

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Right-angled triangle with mathematical formulas

📐 Part 1: Pythagoras' Theorem

1. A ladder is placed 3 metres from the base of a wall and reaches 4 metres up the wall. What is the length of the ladder?

Length = _________ metres

2. A rectangular football field is 100 metres long and 60 metres wide. What is the diagonal distance across the field?

Diagonal distance = _________ metres

3. In a right-angled triangle, if the hypotenuse is 13 cm and one side is 5 cm, what is the length of the third side?

8 cm

12 cm

14 cm

18 cm

4. A ramp for wheelchair access has a horizontal distance of 12 metres and a vertical rise of 1.5 metres. Calculate the length of the ramp.

Ramp length = _________ metres (round to 1 decimal place)

📊 Part 2: Trigonometry (SOHCAHTOA)

5. Which trigonometric ratio would you use to find the angle of elevation when you know the opposite side and adjacent side?

Sine (SOH)

Cosine (CAH)

Tangent (TOA)

6. A flagpole casts a shadow 8 metres long. The angle of elevation from the tip of the shadow to the top of the flagpole is 35°. Calculate the height of the flagpole.

Height = _________ metres (round to 1 decimal place)

7. From a cliff 50 metres high, the angle of depression to a boat is 25°. How far is the boat from the base of the cliff?

Distance = _________ metres (round to 1 decimal place)

8. Complete the SOHCAHTOA definitions:

SOH: Sine = _________ ÷ _________

CAH: Cosine = _________ ÷ _________

TOA: Tangent = _________ ÷ _________

🌏 Part 3: Real-World Applications

9. An Aboriginal tracker needs to find the distance across a river. Standing 30 metres back from the riverbank, the angle of elevation to a tree on the opposite bank is 28°. If the tree is 15 metres tall, what is the width of the river?

River width = _________ metres

10. A surveyor is mapping land for a new community centre. From point A, they measure a bearing of 065° to point B, which is 200 metres away. From point B, they measure a bearing of 155° to point C, which is 150 metres away. Draw a diagram and calculate the direct distance from A to C.

Distance AC = _________ metres

11. Explain in your own words when you would choose to use Pythagoras' theorem versus trigonometric ratios to solve a right-angled triangle problem.