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Byju's Answer
Standard XII
Mathematics
Functions
lf the sides ...
Question
lf the sides of a triangle are
√
2
,
√
6
,
√
8
then the angles of the triangle are
A
30
0
,
75
0
,
75
0
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B
45
0
,
45
0
,
90
0
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C
30
0
,
60
0
,
90
0
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D
60
0
,
60
0
,
60
0
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Solution
The correct option is
C
30
0
,
60
0
,
90
0
Given,
a
=
√
2
,
b
=
√
6
,
c
=
√
8
∴
a
2
+
b
2
=
(
√
2
)
2
+
(
√
6
)
2
=
2
+
6
=
8
=
(
√
8
)
2
=
c
2
→
c
2
=
a
2
+
b
2
Hence the above triangle is a right angled triangle.
Let,
a
=
√
2
b
=
√
6
c
=
√
8
Then,
∠
C
=
90
0
And
sin
A
=
√
2
√
8
=
1
2
Hence,
∠
A
=
30
0
Therefore
∠
B
=
180
0
−
(
90
0
+
30
0
)
=
60
0
.
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