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Byju's Answer
Standard IX
Mathematics
Trigonometric Ratio(sin,cos,tan)
Match the fol...
Question
Match the following if in
Δ
ABC,
∠
B
=
90
0
,
∠
C
=
θ
and AB = 9 cm and BC = 12 cm.
A
c
o
s
e
c
θ
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B
c
o
t
θ
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C
s
e
c
θ
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Solution
Given,
In
Δ
ABC,
∠
B
=
90
0
,
∠
C
=
θ
AB = 9 cm and BC = 12 cm
By pythagoras theorem,
(
A
C
)
2
=
(
A
B
)
2
+
(
B
C
)
2
(
A
C
)
2
=
(
9
)
2
+
(
12
)
2
(
A
C
)
2
=
81
+
144
(
A
C
)
2
=
225
A
C
=
15
c
m
Case 1:
s
i
n
θ
=
A
B
A
C
=
9
15
c
o
s
e
c
θ
=
1
s
i
n
θ
∴
c
o
s
e
c
θ
=
1
9
15
=
15
9
Case 2:
t
a
n
θ
=
A
B
B
C
=
9
12
c
o
t
θ
=
1
t
a
n
θ
∴
c
o
t
θ
=
1
9
12
=
12
9
Case 3:
c
o
s
θ
=
B
C
A
C
=
12
15
s
e
c
θ
=
1
c
o
s
θ
∴
s
e
c
θ
=
1
12
15
=
15
12
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0
Similar questions
Q.
A right angled
Δ
A
B
C
right angled at B, and
A
B
=
b
a
,
B
C
=
a
b
,
∠
C
=
θ
then
a
sin
θ
.
b
cos
θ
is:
Q.
Δ
A
B
C
∼
Δ
P
Q
R
and
A
(
Δ
A
B
C
)
A
(
Δ
P
Q
R
)
=
16
9
. If
P
Q
=
18
cm and
B
C
=
12
cm, then
A
B
and
Q
R
are respectively:
Q.
Assertion :If
a
,
b
,
c
∈
R
+
and are not all equal, then
sec
θ
=
(
b
c
+
c
a
+
a
b
)
(
a
2
+
b
2
+
c
2
)
Reason:
sec
θ
≤
−
1
and
sec
θ
≥
1
Q.
In
Δ
A
B
C
,
if
A
B
=
6
√
3
cm,
A
C
=
12
cm and
B
C
=
6
cm, then angle B is equal to:
Q.
The area of
Δ
A
B
C
in which
A
B
=
B
C
=
4
c
m
and
∠
B
=
90
0
is :
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