Trigonometry Banker

In triangle ABC, AB = 8.4 cm, AC = 6.1 cm and angle BAC = 52°.

1. (a) Calculate BC. Give your answer correct to 3 significant figures. [3]

A triangular plot of land has two sides of length 35 m and 48 m. The angle between these sides is 74°.

1. (a) Calculate the area of the plot. Give your answer correct to the nearest square metre. [2]
2. (b) Grass seed costs Rs 1250 per 10 m². Calculate the cost of seed for the whole plot, using your answer to part (a). [2]

Two sides of a triangle are 5 cm and 7 cm, and the angle between them is 60°.

1. (a) Calculate the length of the third side. Give your answer correct to 3 significant figures. [3]

In triangle ABC, angle BAC = 47°, angle ABC = 68° and BC = 12.5 cm.

1. (a) Calculate AC. Give your answer correct to 3 significant figures. [3]

A triangle has sides of length 7 cm, 9 cm and 12 cm.

1. (a) Calculate the size of the largest angle of the triangle. Give your answer correct to 1 decimal place. [4]

A triangle has area 54 cm². Two of its sides are 9 cm and x cm, and the angle between them is 40°.

1. (a) Find x. Give your answer correct to 3 significant figures. [3]

In triangle ABC, AB = 9.2 cm, BC = 7.4 cm and angle BAC = 48°.

1. (a) Angle ACB is obtuse. Calculate angle ACB, correct to 1 decimal place. [4]
2. (b) Calculate angle ABC. [1]

A field is in the shape of a quadrilateral ABCD. AB = 120 m, BC = 95 m and angle ABC = 108°. The diagonal AC divides the field into two triangles. Angle CAD = 40° and angle ACD = 65°. Keep full calculator values for later parts.

1. (a) Calculate AC. [3]
2. (b) Calculate CD. [3]
3. (c) Calculate the area of the field ABCD, correct to 3 significant figures. [3]

A boat leaves harbour H and sails 14 km on a bearing of 060° to a buoy A. It then sails 9 km on a bearing of 170° to a buoy B.

1. (a) Show that angle HAB = 70°. [2]
2. (b) Calculate the distance HB. [3]
3. (c) Calculate the bearing of B from H, correct to the nearest degree. [3]

Do not use a calculator in this question.

1. (a) A triangle has sides 6 cm and 10 cm with an angle of 30° between them. Find its area. [2]
2. (b) Another triangle has sides 8 cm and 6 cm and area 12√3 cm². Find the two possible sizes of the angle between these sides. [3]

A ladder 6.5 m long leans against a vertical wall on horizontal ground. The ladder makes an angle of 72° with the ground.

1. (a) Calculate how far up the wall the ladder reaches. Give your answer correct to 3 significant figures. [2]

Triangle ABC has a right angle at B. AB = 11.2 cm and BC = 7.3 cm.

1. (a) Calculate angle BAC. Give your answer correct to 1 decimal place. [2]

Usman stands on level ground 45 m from the foot of a vertical minaret. His eyes are 1.6 m above the ground. The angle of elevation of the top of the minaret from his eyes is 38°.

1. (a) Calculate the height of the minaret. Give your answer correct to 3 significant figures. [3]

Ayesha walks 5 km due north and then 3.2 km due east.

1. (a) Calculate how far she is from her starting point. Give your answer correct to 3 significant figures. [2]
2. (b) Calculate the bearing of her final position from her starting point, correct to the nearest 0.1°. [3]

A wheelchair ramp rises 0.75 m. The ramp makes an angle of 4.8° with the horizontal.

1. (a) Calculate the length of the sloping surface of the ramp. Give your answer correct to 3 significant figures. [2]
2. (b) Calculate the horizontal distance covered by the ramp. Give your answer correct to 3 significant figures. [2]

From the top of a vertical cliff 80 m above sea level, the angle of depression of a boat is 32°. The boat sails directly away from the cliff until the angle of depression is 18°.

1. (a) Calculate the distance the boat moves. Give your answer correct to 3 significant figures. [4]

ABCDEFGH is a cuboid. The base ABCD has AB = 8 cm and BC = 6 cm. The vertical edges AE, BF, CG and DH are 5 cm. G is directly above C.

1. (a) Calculate the length of the diagonal AG. Give your answer correct to 3 significant figures. [2]
2. (b) Calculate the angle between AG and the base ABCD. [3]

VABCD is a pyramid with a square base ABCD of side 10 cm. The vertex V is vertically above the centre of the base, and the vertical height is 12 cm.

1. (a) Calculate the length of a sloping edge, VA. Give your answer correct to 3 significant figures. [3]
2. (b) Calculate the angle between VA and the base. [2]

A school field is a horizontal rectangle ABCD with AB = 40 m and BC = 30 m. A vertical flagpole 18 m tall stands at corner A.

1. (a) Calculate the distance AC. [1]
2. (b) Calculate the angle of elevation of the top of the flagpole from C. [2]
3. (c) Calculate the angle of elevation of the top of the flagpole from B. [2]

A cube has edge length a cm. A space diagonal joins two opposite vertices of the cube, passing through its centre.

1. (a) Calculate the angle between a space diagonal of the cube and one of its faces. Give your answer correct to 1 decimal place. [3]

A ramp has a horizontal rectangular base ABCD with AB = 12 m and BC = 7 m. BCFE is a vertical rectangle with BE = CF = 4 m, so E is directly above B and F is directly above C. ADFE is the sloping surface.

1. (a) Calculate the length AF. [3]
2. (b) Calculate the angle between AF and the base ABCD. [2]

Do not use a calculator in this question.

1. (a) Write down the exact value of sin 30°. [1]
2. (b) Write down the exact value of tan 45°. [1]
3. (c) Find the exact value of 4 sin 30° + tan² 60°. [2]

Do not use a calculator in this question.

1. (a) Solve sin x = 0.5 for 0° ≤ x ≤ 360°. [2]
2. (b) Solve cos x = −√3/2 for 0° ≤ x ≤ 360°. [2]

1. (a) Solve 3 cos x + 1 = 0 for 0° ≤ x ≤ 360°. Give your answers correct to 1 decimal place. [3]

Do not use a calculator in this question.

1. (a) For the graph of y = sin x for 0° ≤ x ≤ 360°, write down the coordinates of the maximum point and of the minimum point. [2]
2. (b) sin 40° = 0.643, correct to 3 decimal places. Use the symmetry of the graph to find another angle between 0° and 360° whose sine is 0.643. [1]
3. (c) Write down the value of sin 220°. [1]
4. (d) Write down the range of values of y = 2 cos x + 1 for 0° ≤ x ≤ 360°. [2]

1. (a) Solve tan x = 2.5 for 0° ≤ x ≤ 360°. Give your answers correct to 1 decimal place. [2]
2. (b) Solve 5 sin x + 2 = 0 for 0° ≤ x ≤ 360°. Give your answers correct to 1 decimal place. [3]

1. (a) A right-angled triangle has shorter sides 9 cm and 12 cm. Find the length of the hypotenuse. [2]
2. (b) Another right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the length of the third side. [2]

A phone screen is a rectangle 6.8 cm wide and 14.6 cm tall.

1. (a) Calculate the length of the diagonal of the screen. Give your answer correct to 1 decimal place. [2]

Do not use a calculator in this question.

1. (a) Find the distance between A(−2, 3) and B(4, −5). [2]
2. (b) Show that a triangle with sides 7 cm, 24 cm and 25 cm is right-angled. [2]

ABCD is a kite with AB = AD = 10 cm and CB = CD = 17 cm. The diagonal BD = 16 cm. Do not use a calculator in this question.

1. (a) Calculate the length of the diagonal AC. [4]
2. (b) Calculate the area of the kite. [2]