Unit 3 Quiz: Trigonometry and Geometry
Comprehensive assessment covering all 20 lessons: right-angled and non-right-angled trigonometry, congruence, similarity, area and volume ratios, and circle geometry.
Multiple Choice
Select the best answer for each question. Each question is worth 1 mark.
1 mark In a right-angled triangle, $\sin \theta = \frac{4}{5}$. The value of $\cos \theta$ is:
1 mark The angle of elevation of the sun is $30°$. A 2 m stick casts a shadow of length:
1 mark Which congruence test requires the angle to be included between two sides?
1 mark Two similar cylinders have radii in ratio 1:3. The ratio of their volumes is:
1 mark Corresponding angles between parallel lines are:
1 mark In triangle ABC, a = 6, A = 30°, B = 45°. Side b equals:
1 mark The cosine of an angle in a triangle with sides 5, 12, 13 is:
1 mark The area of a triangle with sides 7, 8 and included angle 120° is:
1 mark In a cyclic quadrilateral, one angle is 100°. The opposite angle is:
1 mark A bearing of 270° is the compass direction:
1 mark The scale factor of a model ship to the real ship is 1:50. If the real ship is 150 m long, the model is:
1 mark If the angle at the centre is 120°, the angle at the circumference subtended by the same arc is:
1 mark Given two sides 8 and 10 and non-included angle 30°, the number of possible triangles is:
1 mark In triangle ABC, a = 5, b = 6, c = 7. Angle B is closest to:
1 mark The exact value of $\sin 30°$ is:
Short Answer
Show all working and justify your answers.
Question 16
From a point A on the ground, the angle of elevation to the top of a tower is $25°$. From a point B, 50 m closer to the tower, the angle of elevation is $40°$.
(a) Draw a diagram and label all known information. (1 mark)
(b) Show that the height of the tower is $\frac{50 \tan 25° \tan 40°}{\tan 40° - \tan 25°}$. (3 marks)
(c) Calculate the height to the nearest metre. (1 mark)
Question 17
Two triangles ABC and DEF are similar with scale factor 2:3. Triangle ABC has sides AB = 8 cm, BC = 10 cm, CA = 12 cm.
(a) Find the lengths of the sides of triangle DEF. (2 marks)
(b) If the area of triangle ABC is 40 cm$^2$, find the area of triangle DEF. (2 marks)
(c) A student claims the perimeter of DEF is 1.5 times the perimeter of ABC. Verify this claim. (1 mark)
Question 18
In quadrilateral ABCD, AB = 6 cm, BC = 8 cm, CD = 10 cm, DA = 12 cm and diagonal AC = 10 cm.
(a) Prove that triangle ABC is right-angled. (2 marks)
(b) Find angle CAD using the cosine rule. (2 marks)
(c) Evaluate whether ABCD is a cyclic quadrilateral. Justify your answer. (1 mark)