State the sine rule for a triangle with sides a, b, c opposite angles A, B, C respectively.
(Total for Question 1 is 1 mark)
2
State the cosine rule used to find the length of side a.
(Total for Question 2 is 1 mark)
3
Calculate the area of a triangle with sides 7 cm and 10 cm, and an included angle of 50 degrees, giving your answer correct to 3 significant figures.
(Total for Question 3 is 2 marks)
4
State the formula for the area of a triangle in terms of two sides p and q and the included angle R.
(Total for Question 4 is 1 mark)
5
In triangle ABC, angle A = 30 degrees and angle B = 90 degrees. State the size of angle C.
(Total for Question 5 is 1 mark)
6
A triangle has all three side lengths known and no angles known. Which rule must be used first to find an angle?
A) Sine rule
B) Cosine rule
C) Area formula
D) Pythagoras' theorem
(Total for Question 6 is 1 mark)
7
In triangle ABC, angle A = 42 degrees and angle B = 97 degrees. Find angle C.
(Total for Question 7 is 1 mark)
8
In triangle ABC, angle A = 42 degrees, angle B = 97 degrees and side a = 6.5 cm (opposite angle A). Calculate side c (opposite angle C), giving your answer correct to 3 significant figures.
(Total for Question 8 is 2 marks)
9
In triangle ABC, b = 9 cm, c = 12 cm and the included angle A = 55 degrees. Calculate side a, giving your answer correct to 3 significant figures.
(Total for Question 9 is 2 marks)
10
A triangle has sides of length 5 cm and 9 cm with an included angle of 110 degrees. Calculate the area of the triangle, giving your answer correct to 3 significant figures.
(Total for Question 10 is 2 marks)
11
In triangle ABC, a = 8 cm, b = 6 cm and c = 11 cm, where angle C is opposite side c. Calculate the size of angle C, giving your answer correct to 1 decimal place.
(Total for Question 11 is 2 marks)
12
In triangle PQR, p = 10 cm, q = 14 cm and angle R = 90 degrees. State the value of sin(R).
(Total for Question 12 is 1 mark)
13
Hence calculate the area of triangle PQR.
(Total for Question 13 is 2 marks)
14
In triangle ABC, angle A = 36 degrees, angle B = 82 degrees and side b = 15 cm (opposite angle B). Calculate side a (opposite angle A), giving your answer correct to 3 significant figures.
(Total for Question 14 is 3 marks)
15
A triangle has two sides of length 11 cm and 15 cm with an included angle of 128 degrees. Calculate the length of the third side, giving your answer correct to 3 significant figures.
(Total for Question 15 is 3 marks)
16
A triangle has sides 9 cm, 13 cm and 17 cm. Calculate the size of the smallest angle, giving your answer correct to 1 decimal place.
(Total for Question 16 is 3 marks)
17
A parallelogram has sides of length 7 cm and 12 cm, with one interior angle of 65 degrees. Calculate the area of the parallelogram, giving your answer correct to 3 significant figures.
(Total for Question 17 is 3 marks)
18
A triangular field has two sides of length 45 m and 60 m, with an angle of 72 degrees between them. A path runs along the third side of the field.
(a)Calculate the length of the path (the third side of the field), giving your answer correct to 3 significant figures.(2)
(b)Calculate the area of the field, giving your answer correct to 3 significant figures.(2)
(Total for Question 18 is 4 marks)
19
A cargo ship sails from harbour A on a bearing of 048 degrees for a distance of 20 km to reach point B. At B, the ship changes course and sails on a bearing of 142 degrees for a distance of 16 km to reach point C.
(a)Show that angle ABC = 86 degrees.(1)
(b)Calculate the distance AC, giving your answer correct to 3 significant figures.(2)
(c)Find the bearing of C from A, giving your answer to the nearest degree.(2)
(Total for Question 19 is 5 marks)
Mark scheme · G5D Sine Rule, Cosine Rule and Area of a Triangle: Fluency and Exam Drill
Question 1
B1 a/sin(A) = b/sin(B) = c/sin(C) oe (reciprocal form also accepted)
Answer: a/sin(A) = b/sin(B) = c/sin(C)
Question 2
B1 a2 = b2 + c2 - 2bc*cos(A) oe
Answer: a2 = b2 + c2 - 2bc*cos(A)
Question 3
M1 Area = 1/2 * 7 * 10 * sin(50)
A1 26.8 cm2 awrt
Answer: 26.8 cm2
Question 4
B1 Area = 1/2 * p * q * sin(R) oe
Answer: Area = (1/2)*p*q*sin(R)
Question 5
B1 60 degrees cao
Answer: 60 degrees
Question 6
B1 B cao
Answer: B) Cosine rule
Question 7
B1 41 degrees cao
Answer: 41 degrees
Question 8
M1 correct sine rule setup: c/sin(41) = 6.5/sin(42), using angle C = 180 - 42 - 97 = 41
M1 recognises the area of a parallelogram with sides p, q and included angle θ is Area = p*q*sin(θ) (twice the area of the triangle formed by a diagonal)