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Mathematics · Self Assessment

Practice Test: Right-Angled Trigonometry & Sine/Cosine Rule

A 100-mark paper covering "Right-Angled Trigonometry" and "Sine Rule, Cosine Rule & Area of a Triangle" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.The hypotenuse of a right-angled triangle is always:Basic2 pts

A. The longest side, opposite the right angle

B. The shortest side

C. Always horizontal

D. Different depending on the angle used

2.sin θ is defined as:Basic2 pts

A. Adjacent ÷ hypotenuse

B. Opposite ÷ adjacent

C. Opposite ÷ hypotenuse

D. Hypotenuse ÷ opposite

3.tan θ is defined as:Basic2 pts

A. Adjacent ÷ hypotenuse

B. Opposite ÷ adjacent

C. Opposite ÷ hypotenuse

D. Hypotenuse ÷ adjacent

4.A 5 m ladder makes a 60° angle with the ground. The height it reaches up a wall is closest to:Intermediate2 pts

A. 2.50 m

B. 5.00 m

C. 8.66 m

D. 4.33 m

5.A right triangle has opposite = 6 cm and adjacent = 8 cm. The angle θ is closest to:Intermediate2 pts

A. 53.1°

B. 36.9°

C. 45.0°

D. 30.0°

6.sin 30° exactly equals:Basic2 pts

A. √3/2

B. 1

C. 0

D. 1/2

7.The angle of elevation is measured:Basic2 pts

A. Downward from the horizontal

B. From the vertical only

C. Upward from the horizontal

D. Always exactly 90°

8.The sine rule states:Basic2 pts

A. a/sin A = b/sin B = c/sin C

B. a² = b² + c² − 2bc cos A

C. Area = ½ab sin C

D. a² + b² = c²

9.The cosine rule should be used when you know:Intermediate2 pts

A. Two angles and a side only

B. Only one side

C. Nothing about the triangle

D. Two sides and the included angle, or all three sides

10.The formula for the area of a triangle using two sides and the included angle is:Intermediate2 pts

A. ½ base × height only

B. ½ab sin C

C. abc

D. a² + b²

11.Triangle ABC has a = 7 cm, b = 9 cm, and angle B = 72°. Angle A is closest to:Advanced2 pts

A. 47.7°

B. 72.0°

C. 90.0°

D. 132.3°

12.The "ambiguous case" in trigonometry can occur when using:Advanced2 pts

A. The cosine rule for a side

B. The area formula

C. The sine rule to find an angle from SSA data

D. Pythagoras' theorem

13.A triangle has sides of 6 cm and 9 cm with an included angle of 50°. Its area is closest to:Advanced2 pts

A. 27.0 cm²

B. 54.0 cm²

C. 20.7 cm²

D. 41.4 cm²

14.The cosine rule formula is:Intermediate2 pts

A. a² = b² + c² − 2bc cos A

B. a/sin A = b/sin B

C. Area = ½ab sin C

D. a² + b² = c²

15.A triangle has sides a = 5, b = 7, c = 10. The angle C (opposite the longest side) will be:Advanced2 pts

A. Acute

B. Exactly 90°

C. Impossible to determine

D. Obtuse

Section B — True / False

20 marks

10 questions · 2 marks each.

16.The hypotenuse label never changes, regardless of which angle is being used.Basic2 pts

True

False

17.cos θ = opposite ÷ hypotenuse.Basic2 pts

True

False

18.To find a missing angle from two known sides, you should use an inverse trig function.Intermediate2 pts

True

False

19.tan 45° exactly equals 1.Basic2 pts

True

False

20.The angle of elevation and the angle of depression between two observers looking directly at each other are always equal.Intermediate2 pts

True

False

21.The sine rule and cosine rule are needed for triangles that do not necessarily have a right angle.Basic2 pts

True

False

22.In standard triangle labelling, side a is adjacent to angle A.Intermediate2 pts

True

False

23.The cosine rule can be used to find an angle when all three sides of a triangle are known.Intermediate2 pts

True

False

24.A negative value inside cos⁻¹ during the cosine rule always means a calculation error has occurred.Advanced2 pts

True

False

25.In the ½ab sin C formula, C must be the angle included between sides a and b.Intermediate2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.The mnemonic for the three trigonometric ratios is SOH-CAH-______.Basic2 pts

27.cos θ = adjacent ÷ ______.Basic2 pts

28.To find a missing side using an angle and the hypotenuse, opposite = hypotenuse × ______.Intermediate2 pts

29.sin 90° exactly equals ______.Basic2 pts

30.The angle measured downward from the horizontal to a point below the observer is called the angle of ______.Basic2 pts

31.In standard triangle labelling, side a is opposite angle ______.Basic2 pts

32.The area formula using two sides and the included angle is Area = ½ab sin ______.Intermediate2 pts

33.The cosine rule formula is a² = b² + c² − 2bc cos ______.Intermediate2 pts

34.If a calculator gives an angle of 40° in an ambiguous sine rule case, the second possible value is ______ degrees.Advanced2 pts

35.When two sides and the included angle are known (SAS), you should use the ______ rule.Intermediate2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

SOH

CAH

TOA

Sine rule

Cosine rule

Column B

tan θ = opposite ÷ adjacent

sin θ = opposite ÷ hypotenuse

a² = b² + c² − 2bc cos A

cos θ = adjacent ÷ hypotenuse

a/sin A = b/sin B = c/sin C

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain how to decide which trigonometric ratio (sin, cos or tan) to use in a right-angled triangle problem.Advanced4 pts

42.Describe what an angle of elevation is.Intermediate4 pts

43.Explain when you should use the cosine rule instead of the sine rule.Advanced4 pts

44.Describe what the "ambiguous case" of the sine rule means.Advanced4 pts

45.Explain how to find the area of a triangle when you know two sides and the angle between them.Intermediate4 pts

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