Question 1: In a right angles triangle , right angled at
, if
, find all the six trigonometric ratios of
.
Answer:
Given
Therefore,
;
;
;
Question 2: If
, find the value of the other five trigonometric ratios.
Answer:
Given
By Pythagoras theorem, we have
;
;
;
Question 3: If , find the value of
Answer:
Given , therefore by Pythagoras theorem,
;
;
Hence
Question 4: If , show that
Answer:
Given
By Pythagoras theorem, we have
and
Hence,
Question 5: In , right angles at
, if
and
, show that
Answer:
Given
By Pythagoras theorem, we have
and
and
LHS = RHS.
Hence proved.
Question 6: If
, prove that
Answer:
Given
By Pythagoras theorem, we have
;
;
LHS
RHS
Therefore LHS = RHS. Hence proved.
Question 7: In the given figure, and
. Determine (i)
ii)
iii)
iv)
Answer:
By Pythagoras theorem, we have
Therefore:
i)
ii)
iii)
iv)
Question 8: In a , right angles at
and
, i) is
ii) is
Answer:
Given
i)
ii)
Question 9: If , show that
Answer:
LHS
RHS. Hence proved.
Question 10: If
, find the value of
Answer:
Squaring on both sides,
Question 11: If
, evaluate i)
ii)
Answer:
i)
ii)
Question 12: If , check if
Answer:
Given
LHS
RHS
Therefore LHS = RHS. Hence proved.
Question 13: If
, find the value of
Answer:
Given
Dividing both the numerator and denominator by we get
Question 14: If
, find
Answer:
By Pythagoras theorem,
Therefore,
and
Hence
Question 15: If
, find the value of
Answer:
By Pythagoras theorem,
Therefore
;
;
;
Question 16: If
; evaluate
Answer:
By Pythagoras theorem we get
Therefore
;
;
Therefore
Question 17: If
, verify
Answer:
By Pythagoras theorem we get
Therefore
;
;
LHS
RHS =
Therefore LHS = RHS. Hence proved.
Question 18: If
, prove that
Answer:
Given
By Pythagoras theorem,
Therefore
;
;
;
;
LHS =
Question 19: If , find
Answer:
Given
By Pythagoras theorem, we get
Therefore
and
Hence
Question 20: If , find
Answer:
Given , find
Question 21: If and
are acute angles such that
, then show that
Answer:
Since
(angles opposite equal sides of a triangle are equal)
Question 22: In a triangle, and
are acute angles such that
, show that
Answer:
and
Given that
(angles opposite equal sides of a triangle are equal)
Question 23: If is an acute angle such that
, find the value of
Answer:
Given
Therefore
By Pythagoras theorem,
and
Hence,
Question 24: In adjoining figure, is right angles at
and
is the midpoint of
.
,
and
. Find i)
ii)
iii)
Answer:
By Pythagoras theorem
Therefore i)
ii) By Pythagoras theorem
Therefore
and
iii)