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Year 9 · Practice

Introductory Trigonometry — Year 9 Practice Questions

Work through these Year 9 practice questions on introductory trigonometry. Try each one before revealing the worked solution.

Questions

1
[2 marks] Easy Ratios

Write down the three trigonometric ratios using SOH CAH TOA.

2
[2 marks] Medium Ratio

In a right-angled triangle the side opposite the angle is 4 and the hypotenuse is 8. Find the sine of the angle.

3
[2 marks] Medium Inverse

Find the angle whose tangent is 1.

4
[3 marks] Medium Finding a side

A right-angled triangle has an angle of 30° with hypotenuse 10 cm. Find the opposite side. Use sin 30° = 0.5.

5
[3 marks] Hard Finding an angle

A right-angled triangle has opposite 6 and adjacent 8. Find the angle. Use tan⁻¹(0.75) ≈ 36.9°.

6
[1 marks] Easy Choosing a ratio

Which ratio links the opposite side and the hypotenuse?

7
[3 marks] Hard Finding a side

A right-angled triangle has an angle of 60° and adjacent side 5 cm. Find the hypotenuse. Use cos 60° = 0.5.

8
[3 marks] Hard Context

A ramp has opposite 3 m and adjacent 4 m. Find the angle it makes with the ground. Use tan⁻¹(0.75) ≈ 36.9°.

Answers & Worked Solutions

Question 1 Solution

Step 1: SOH: sine = opposite ÷ hypotenuse.

Step 2: CAH: cosine = adjacent ÷ hypotenuse; TOA: tangent = opposite ÷ adjacent.

Answer: sin = O/H, cos = A/H, tan = O/A

Question 2 Solution

Step 1: sin = opposite ÷ hypotenuse = 4 ÷ 8.

Step 2: = 0.5.

Answer: 0.5

Question 3 Solution

Step 1: Use tan⁻¹(1).

Step 2: tan⁻¹(1) = 45°.

Answer: 45°

Question 4 Solution

Step 1: sin 30° = opposite ÷ 10.

Step 2: opposite = 0.5 × 10 = 5 cm.

Answer: 5 cm

Question 5 Solution

Step 1: tan of the angle = 6 ÷ 8 = 0.75.

Step 2: angle = tan⁻¹(0.75) ≈ 36.9°.

Answer: 36.9°

Question 6 Solution

Step 1: Opposite and hypotenuse appear in SOH.

Step 2: So the ratio is sine.

Answer: Sine

Question 7 Solution

Step 1: cos 60° = adjacent ÷ hypotenuse, so 0.5 = 5 ÷ h.

Step 2: h = 5 ÷ 0.5 = 10 cm.

Answer: 10 cm

Question 8 Solution

Step 1: tan of the angle = 3 ÷ 4 = 0.75.

Step 2: angle = tan⁻¹(0.75) ≈ 36.9°.

Answer: 36.9°

Topic Overview

Revision Notes

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