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NDA Math Properties of Triangles
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© examsnet.com
Question : 5
Total: 16
The sides of a triangle are
m
,
n
and
√
m
2
+
n
2
+
m
n
. What is the sum of the acute angles of the triangle?
[NDA-I 2021]
45
∘
60
∘
75
∘
90
∘
Validate
Solution:
👈: Video Solution
Concept
Cosine rule:
cos
θ
=
a
2
+
b
2
−
c
2
2
a
b
Where
a
,
b
and
c
are the sides of the triangle and
θ
is the angle between the sides a and
b
.
Calculation:
Let
m
=
n
=
1
unit
Then
√
m
2
+
n
2
+
m
n
=
√
3
unit
√
m
2
+
n
2
+
m
n
=
√
3
Using cosine rule;
cos
θ
=
1
2
+
1
2
−
√
3
2
2
×
1
×
1
⇒
cos
θ
=
−
1
∕
2
∴
θ
=
120
∘
Now, the sum of the acute angles of the triangle
=
180
∘
−
120
∘
=
60
∘
© examsnet.com
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