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Homework answers / question archive / TRIGONOMETRY a) right angled triangle b) 3D problems c) sine, tan, cos d) sine and cosine rules 16) A helicopter flies from its base B to deliver supplies to two oil rigs at C and D
TRIGONOMETRY
a) right angled triangle
b) 3D problems
c) sine, tan, cos
d) sine and cosine rules
16) A helicopter flies from its base B to deliver supplies to two oil rigs at C and D. C is 6km due east of B and the distance from C to D 1s 8km. D is on a bearing of 120° from B.
Find the bearing of D from C.
13) Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm2.
Calculate AC.
11) A triangle has sides of length 2cm, 8cm and 9cm.
Calculate the value of the largest angle in this triangle.
4) Ac = 8 cm
Angle BAC = 28° ÐB is 90°
Calculate the length of AB.
14) PQR is a triangle.
ÐP = 66°, ÐQ = 37° and ÐR = 77°
QP length is 12.5 cm
Calculate PR.
21) ABCD is a kite.
The diagonals AC and BD intersect at x.
AC = 12 cm, BD = 20 cm and DX:XB = 3:2.
(a) Calculate angle ABC.
(b) Calculate the area of the kite.
21) In triangle ABC, AB = 6 cm, BC = 4cm and angle BCA = 65°.
Calculate
(a) angle CAB,
(b) The area of triangle ABC.
18) In triangle ABC, AB = 6cm, BC = 13cm and angle ACB = 23°.
Calculate angle BAC, which is obtuse.
9) The line AB represents the glass walkway between the Petronas Towers in Kuala Lumour.
The walkway is 58.4 metres long and is 170 metres above the ground.
The angle of elevation of the point P from A is 78.3°.
Calculate the height of P above the ground.
12) A helicopter files 8 Km due north from A to B. It then flies 5 km from B to c returns to A. Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
(b) find the bearing of A from C.
21) The diagram shows 3 ships A, B and C at sea.
AB = 5km, BC = 4.5 km and AC = 2.7 km.
(a) Calculate angle ACB.
Show all your working.
(b) The bearing of A from C is 220°.
Calculate the bearing of B from C.
1) In the right-angled triangle ABC, cos C = 4/5. Find angle A.
7 (a) The diagram shows a circle with two chords, AB and CD, intersecting at X.
(i) Show that triangles ACX and DBX are similar.
Answer(a){i)
(ii) AX=3.2cm, BX= 12.5cm, CX =4cm and angle AXC = 110°.
(a) Find DX.
(b) Use the cosine rule to find AC.
(c) Find the area of triangle BXD.
(b) In the diagram, BC represents a building 30m tall.
A flagpole, DC, stands on top of the building.
From a point, A, the angle of elevation of the top of the building is 31°.
The angle of elevation of the top of the flagpole is 37°.
Calculate the height, DC, of the flagpole.
8)
North
NOT TO
SCALE
P $8 km
L
74km
Y
A ship sails from port P to port Q.
Q is 74km from P on a bearing of 142°.
A lighthouse, L, is 58km from P on a bearing of 110°.
(a) Show that the distance LQ is 39.5 km correct to | decimal place.
Answer(a)
(3)
(b) Use the sine rule to calculate angle PQL.
(c) Find the bearing of
(i) P from Q,
(ii) L from Q.
(d) The ship takes 2 hours and 15 minutes to sail the 74km from P two Q.
Calculate the average speed in knots.
[1 knot = 1.85 km/h]
(e) Calculate the shortest distance from the lighthouse to the path of the ship.
1 (a) ABCD is a trapezium.
AB = 11 cm
DC = 17 cm
DE = 2.6 cm
AE = 4.7 cm
(i) Calculate the length of AD.
(ii) Calculate the size of angle BCD.
(iii) Calculate the area of the trapezium ABCD.
(b) A similar trapezium has perpendicular height 9.4 cm.
Calculate the area of this trapezium.
16) The diagram shows a quadrilateral ABCD.
Angle BAD = 49° and angle ABD = 55°.
BD = 80 cm, BC = 95 m and CD = 90 m.
(a) Use the sine rule to calculate the length of AD.
(b) Use the cosine rule to Calculate angle BCD.
3) (a)
The diagram shows triangle PQR with PQ = 12cm and PR = 17 cm.
The area of triangle PQR is 97 cm2 and angle QPR is acute.
i) Calculate angle QPR.
ii) The midpoint of PQ is X.
Use the cosine rule to calculate the length of XR.
