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Standard VII
Mathematics
Question
ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :
s
i
n
45
∘
is
1
√
m
, m is
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Solution
Verified by Toppr
Given:
△
A
B
C
,
A
B
=
B
C
=
x
,
∠
A
B
C
=
90
∘
By Pythagoras Theorem,
A
C
2
=
A
B
2
+
B
C
2
A
C
2
=
x
2
+
x
2
A
C
2
=
2
x
2
A
C
=
√
2
x
Since,
A
B
=
B
C
, then by Isosceles triangle property,
∠
A
C
B
=
∠
C
A
B
=
45
∘
Now,
S
i
n
45
∘
=
S
i
n
C
=
A
B
A
C
=
x
x
√
2
=
1
√
2
∴
m
=
2
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