MENU
Educational Resources
Exam Papers
Form 1 Videos
Form 2 Videos
Form 3 Videos
Form 4 Videos
Grade 4 Videos
Grade 5 Videos
Grade 6 Videos
Grade 7 Videos
Class 8 Videos
Form 1 Exams
Form 2 Exams
Form 3 Exams
Form 4 Exams
KCSE Videos
Class 8 Exams
Grade 5 Exams
Grade 4 Exams
Grade 3 Exams
Grade 2 Exams
Grade 1 Exams
Online Tests
Online Tuition
Sign In
Join
Get access to thousands of educational resources
Get premium membership
and access revision papers with marking schemes, video lessons and live classes.
OR
Processing. Please wait.
Form 3 Mathematics: Trigonometry II Questions and Answers
Given that tan75 =
2
+
√
3
find tan 165 in the form
a
+
b
√
c
.
(3m 29s)
1145 Views
SHARE
|
« Previous
Next »
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
×
Share Content Via:
Facebook
Twitter
WhatsApp
Close
Get premium membership