The diagram shows the positions of three points , and in a field.
Show that is 118.1 m, correct to 1 decimal place.
Calculate angle .
Angle ................................................
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Syllabus Edition
First teaching 2021
Last exams 2024
The diagram shows the positions of three points , and in a field.
Show that is 118.1 m, correct to 1 decimal place.
Calculate angle .
Angle ................................................
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The diagram shows two triangles.
Calculate QR.
QR = ............................................ m
Calculate RS.
RS = ............................................ m
Calculate the total area of the two triangles.
............................................ m2
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Use the cosine rule to find angle BAC.
Angle BAC = ...................................................
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The diagram shows triangle ABC.
BC = ............................................... m [4]
Angle ACB = ................................................... [3]
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The diagram shows a field, ABCD, on horizontal ground.
Use the cosine rule to find angle BAC.
Angle BAC = ...................................................
Use the sine rule to find angle CAD.
Angle CAD = ...................................................
Calculate the area of the field.
............................................... m2
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Calculate the area of triangle PQR.
........................................ cm2
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The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m and BD = 168 m.
Angle CBD rounds to 106.0°, correct to 1 decimal place.
Calculate the area of triangle BCD.
............................................ m2
Tomas buys the triangular part of the field, BCD.
The cost is $35 750 per hectare.
Calculate the amount he pays.
Give your answer correct to the nearest $100.
[1 hectare = 10000m2]
$ ................................................
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The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m and BD = 168 m.
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AD = 10 cm, BC = 8 cm, BX = 5 cm, CX = 7 cm.
The diagonals of the cyclic quadrilateral ABCD intersect at X.
Calculate angle BXC.
Angle BXC = ................................................
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The diagram shows a trapezium .
is parallel to .
, , angle and angle .
Calculate .
........................................... m
Calculate .
........................................... m
Calculate the area of .
.......................................... m2
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The diagram shows two triangles and .
and .
Angle , angle and angle .
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In the diagram, is a vertical wall standing on horizontal ground .
is the point on where = 58 m.
The angle of elevation of from is 26°.
The angle of elevation of from is 72°.
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In the diagram, AB = 18 cm, BC = 21.3 cm and BD = 11.6 cm.
Angle BDC = 123.5° and angle ABC is a right angle.
Angle BCD = ............................................... [3]
AD = ......................................... cm [5]
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The diagram shows the positions of three cities, Geneva (G), Budapest (B) and Hamburg (H).
Use the cosine rule to calculate the distance from Geneva to Budapest.
.......................................... km
The bearing of Budapest from Hamburg is 133°.
Calculate the bearing of Budapest from Geneva.
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Calculate angle ACB.
Angle ACB = .................................................
Calculate angle ACD.
Angle ACD = ..................................................
Calculate the area of the quadrilateral ABCD.
........................................... cm2
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In the pentagon , angle = angle = 90°.
Triangle is equilateral with side length 12 cm.
= = 6 cm.
Calculate angle .
Angle = .............................................
Calculate the area of the pentagon.
......................................... cm2
Calculate.
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The diagram shows a quadrilateral formed from two triangles, and .
Calculate
............................................ cm [3]
............................................ cm [3]
........................................... cm2 [4]
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The diagram shows triangle ABC with point G inside.
CB = 11 cm, CG = 5.3 cm and BG = 6.9 cm.
Angle CAB = 42° and angle ACG = 54°.
Calculate the value of .
................................................
Calculate AC.
AC = ........................................... cm
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The area of triangle DEF is 70 m2.
[4]
= .......................... or = .......................... [4]
DE = ............................................... m [1]
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The diagram shows a field ABCDE.
Calculate the perimeter of the field ABCDE.
................................................ m
Calculate angle ABD.
Angle ABD = ..........................................................
Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
...................................... hectares
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Triangle has an area of 70 m2.
and angle =40°.
Calculate .
= .......................................... m
A different triangle also has an area of 70 m2.
and
Find angle .
Angle = ..............................................
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The diagram shows a design made from a triangle AOC joined to a sector OCB.
AC = 8cm, OB = OC = 7 cm and angle ACO = 78°.
Use the cosine rule to show that OA = 9.47 cm, correct to 2 decimal places.
Calculate angle OAC.
Angle OAC = ................................................
The perimeter of the design is 29.5 cm.
Show that angle COB = 41.2°, correct to 1 decimal place.
Calculate the total area of the design.
......................................... cm2
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The diagram shows two ports, L and P, and a buoy, M.
The bearing of L from P is 201° and LP = 248 km.
The bearing of M from P is 127°.
Angle PML = 42°.
Use the sine rule to calculate LM.
LM = ......................................... km
A ship sails directly from L to P.
Calculate the shortest distance from M to LP.
.......................................... km
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