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# Form 3 Mathematics: Trigonometry II Questions and Answers

Form 3 Mathematics: Trigonometry II Questions and Answers.

Answers are in video format.

Lessons (**30**) * SHARE*

- 1.
Two sides of a triangular field are 21 m and 32 m long. Its area is #240m^2#.The angle between two sides is obtuse. Determine this angle.

2m 42s - 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 #576m^2#, find the perimeter of the plot.

7m 16s - 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.

3m 43s - 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.

6m 2s - 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#.

6m 22s - 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 .

5m 18s - 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.

5m 26s - 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

4m 56s - 9.
Given that tan #75^0 = 2 + sqrt3#, find without using tables tan #15^0# in the form #p+ qsqrtm#, where p, q and m are integers.

2m 53s - 10.
Given that sin a = #1/sqrt5# where a is an acute angle find, without using mathematical tables:
a) Cos a in the form of #asqrtb#, where a and b are rational numbers
b) Tan (90-a)

2m 27s - 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

6m 0s - 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

3m 44s - 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.

11m 26s - 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.

4m 42s - 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

11m 27s - 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

8m 9s - 17.
Given that Cos q = #15/17# and #270^0 le q le360^0#. Find without using tables the values of sine q and tangent q.

2m 57s - 18.
In the triangle below, find the value of m.

1m 44s - 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

2m 59s - 20.
Simplify the following without using tables;
#Tan 45^0 + cos 45 sin 60^0#

4m 32s - 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

7m 58s - 22.
Given that #cos theta#= –0.8070 , find ? for # 0lethetale720 #

5m 59s - 23.
Solve for #theta# without using table given that #0 le theta le 90^o# and that #sin ( 2theta - 30^0) – cos 4theta=0#

1m 14s - 24.
Given that #Sin (x+ 60^0) = Cos (2x)^0#, find #Tan (x+60)^0#

1m 31s - 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.

4m 7s - 26.
A triangle XYZ in which, XY=12.4cm,YZ =15.6cm and angle #YXZ =60^0# is inscribed in a circle. Calculate the radius of the circle correct to 1 decimal place.

2m 15s - 27.
Solve the equation: for Sin (2x+10) =#sqrt3/2 #for #0lexle360^0#

5m 9s - 28.
A triangle ABC is such that AB = 12 cm, angle #CAB =45^0# and angle #ABC = 60^0# . Calculate the area of the triangle ABC.

4m 34s - 29.
Given that tan75 = #2 +sqrt3# find tan 165 in the form #a +bsqrt(c.)#

3m 29s - 30.
Without using tables evaluate
#(cos 30)/(tan 60-sin 45 )#

5m 51s