Question 1: Evaluate each of the following:
Answers:
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
Question 2: Find the value of in each of the following when
:
Answers:
i)
ii)
iii)
iv)
v)
vi)
vii)
Question 3: If is an acute angle and
, find the value of
.
Answers:
Given
Therefore
Hence
Question 4: if , verify that
Answers:
i)
Given
Therefore
;
Therefore LHS
Therefore RHS = LHS. Hence proved.
ii)
Given
Therefore
;
RHS
LHS
Therefore LHS = RHS. Hence proved.
iii)
LHS
RHS = =
iv)
LHS
RHS
Question 5: Find an acute angle when
Answers:
Given
Applying componendo and dividendo we get
Question 6: If and
, then find
.
Answers:
Given
… … … … … i)
Similarly,
… … … … … ii)
Solving i) and ii) we get
and
Question 7: is a right triangle, right angled at
. If
and
units, find remaining two sides and
in
.
Answers:
Given and
Since
units
Similarly,
units
Hence units,
units and
Question 8: A rhombus of side cm has two angles of
each. Find the length of the diagonals.
Answers:
Given is a rhombus.
cm
Property of rhombus: Diagonals are perpendicular bisectors and and
are bisectors of
and
Similarly,
Therefore cm and
cm
Question 9: An equilateral triangle is inscribed in a circle of radius $latex 6 cm. Find the side.
Answers:
Given cm
, then
is the mid point of
and
are bisectors of
and
.
therefore
In we have
and
cm
Therefore
cm
cm
Question 10: If each of and
are positive acute angle, such that
,
and
, find the value of
and
Answers:
Given
… … … … … i)
Similarly,
… … … … … ii)
and
… … … … … iii)
Adding i) , ii) and iii) we get
… … … … … iv)
Now iv) – i)
iv) – ii)
iv) – i)
Question 11: In an acute angles triangle , if
and
, find the value of
and
.
Answers:
Given
… … … … … i)
Also
… … … … … ii)
Adding i) and ii) we get
Substituting in ii) we get
… … … … … iii)
We know
… … … … … iv)
Adding iii) and iv) we get
Therefore
Hence and
Question 12: Evaluate
Answers:
Question 13: Evaluate:
Answers:
Question 14: Find the value of i)
ii)
Answers:
i)
ii)
Question 15: If , verify
i)
ii)
iii)
Answers:
Given we have
;
;
;
i) LHS
RHS
Therefore LHS = RHS. Hence proved.
ii) LHS
RHS
Therefore LHS = RHS. Hence proved.
iii) LHS
RHS
Therefore LHS = RHS. Hence proved.
Question 16: If and
, find the value of
and
Answers:
i)
ii)
Question 17: In a right angled triangle, right angled at , if
,
units, find the remaining angles and sides.
Answers:
Given and
Therefore
units
units
Question 18: If and
and
, find
and
.
Answers:
Given
… … … … … i)
Similarly,
… … … … … ii)
Solving i) and ii) and
Question 19: If
and
and
. Find
and
.
Answers:
Given
… … … … … i)
Also
… … … … … ii)
Solving i) and ii) and
Question 20: In , right angled at
. Find values of i)
ii)
Answers:
We have
i)
ii)
Question 21: If and
are acute angles such that
and
and
. Find
.
Answers:
RHS
Therefore
Question 22: In adjoining figure is a right angled triangle at
and
is a right angled triangle at
. If
and
, find
.
Answers:
Therefore
cm