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Form 3 Mathematics: Trigonometry II Questions and Answers
Simplify the following without using tables;
tan
45
0
+
cos
45
sin
60
0
(4m 32s)
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1.
Two sides of a triangular field are 21 m and 32 m long. Its area is
240
m
2
.The angle between two sides is obtuse. Determine this angle.
2.
Two sides of a triangular plot of land are 52m and 28m. Given that the angle between these two sides is an obtuse angle and that the area of the plot is
576
m
2
, find the perimeter of the plot.
3.
In the figure below AB and BC are chords of a circle, center O. AB = 3cm, BC = 8cm and OC = 5cm.Calculate angle ABC.
4.
Three towns P, Q and R are such that Q is 40 km on the bearing of
290
0
from P. Town R is directly to the south of P. The distance between Q and R is 60km.Find the bearing of Q directly from R.
5.
A ship P is due south of a lighthouse L. A ship Q is 4.8km due east of L. The bearing of Q from P is
030
0
. P sails directly towards Q. Find the distance of P from L when its bearing from L is
110
0
.
6.
A man walks 5km on a bearing of
315
0
from a point A and then walks due south to a B point which is 8km from A. Calculate the bearing of B from A .
7.
Shopping centers X, Y and Z are such that Y is 12 km south of X and Z is 15 km from X.Z is on a bearing of
330
0
from Y. Calculate the bearing of Z from X.
8.
A triangular plot ABC is such that AB = 36m, BC = 40m and AC = 42 m Calculate the: (i) Area of the plot in square metres (ii) Acute angle between the edges AB and BC
9.
Given that tan
75
0
=
2
+
√
3
, find without using tables tan
15
0
in the form
p
+
q
√
m
, where p, q and m are integers.
10.
Given that sin a =
1
√
5
where a is an acute angle find, without using mathematical tables: a) Cos a in the form of
a
√
b
, where a and b are rational numbers b) Tan (90-a)
11.
In the figure below PQRS is a trapezium with SR parallel to PQ. SR = 5cm, RQ = 4cm, QS = 8cm and PQ = 10cm. Calculate: a) The size of angle QSR b) The area of triangle PQ
12.
The figure below shows a quadrilateral ABCD in which AB = 8 cm, DC = 12 cm, < BAD =
45
0
< CBD =
90
0
and BCD =
30
0
Find: (a) The length of BD (b) The size of the angle ADB
13.
A boat at point x is 200 m to the south of point Y. The boat sails from x to another point Z. Point Z is 200m on a bearing of
310
0
from X, Y and Z are on the same horizontal plane. a) Calculate the bearing and the distance of Z from Y b) W is the point on the path of the boat nearest to Y. Calculate the distance WY c) A vertical tower stands at point Y.
14.
In the figure below angle A =
62
0
, angle B =
41
0
, BC = 8.4 cm and CN is the bisector of angle ACB. Calculate the length of CN to 1 decimal place.
15.
In the figure below (not drawn to scale) AB=8cm, AC=6cm, AD= 7cm, CD=2.82cm and angle CAB =
50
0
Calculate to 2 decimal places: (a) The length BC (b) The size of angle ABC; (c) The size of angle CAD; (d) The area of triangle ACD
16.
Given that Sin A=
4
5
,cos B =
5
13
, where A and B are acute angles, without using a calculator or mathematical tables calculate; Sin B cosA +sin A tanB
17.
Given that Cos q =
15
17
and
270
0
≤
q
≤
360
0
. Find without using tables the values of sine q and tangent q.
18.
In the triangle below, find the value of m.
19.
In the figure below BC is perpendicular to AD, CD = 8, the measure of angle D is 60° and the measure of angle A is 45°. Find the length of AB
20.
Simplify the following without using tables;
tan
45
0
+
cos
45
sin
60
0
21.
In the figure below DA is a diameter of the circle ABCD Center O, radius 10cm. TCS is a tangent to the circle at C, AB=BC and angle DAC=
38
0
a) Find the size of the angle; (i) ACS; (ii) BCA b) Calculate the length of: (i) AC (ii) AB
22.
Given that
cos
θ
= –0.8070 , find ? for
0
≤
θ
≤
720
23.
Solve for
θ
without using table given that
0
≤
θ
≤
90
o
and that
sin
(
2
θ
-
30
0
)
–
cos
4
θ
=
0
24.
Given that
sin
(
x
+
60
0
)
=
cos
(
2
x
)
0
, find
tan
(
x
+
60
)
0
25.
In the triangle below, AB =8.4 cm and the angles at A and B are
48
0
and
54
0
respectively. Calculate the area of the triangle.
26.
A triangle XYZ in which, XY=12.4cm,YZ =15.6cm and angle
Y
X
Z
=
60
0
is inscribed in a circle. Calculate the radius of the circle correct to 1 decimal place.
27.
Solve the equation: for Sin (2x+10) =
√
3
2
for
0
≤
x
≤
360
0
28.
A triangle ABC is such that AB = 12 cm, angle
C
A
B
=
45
0
and angle
A
B
C
=
60
0
. Calculate the area of the triangle ABC.
29.
Given that tan75 =
2
+
√
3
find tan 165 in the form
a
+
b
√
c
.
30.
Without using tables evaluate
cos
30
tan
60
-
sin
45
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