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