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Byju's Answer
Standard IX
Mathematics
If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side
In A B C, if ...
Question
In
∆
ABC, if
∠A = 90°, which is the longest side?
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Solution
I
n
∆
A
B
C
,
∠
A
=
90
°
.
The sum of the other two angles must be such that
∠
A
+
∠
B
+
∠
C
=
180
°
⇒
∠
B
+
∠
C
=
90
°
(
∵
∠
A
=
90
°
)
Thus, angles B and C both measure less than 90
°
.
Angle A is the largest in the triangle and the side opposite to it, i.e., BC is the longest.
∴ BC is the hypotenuse of the right triangle ABC.
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In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?