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If Two Angles of a Triangle Are Unequal Then the Side Opposite to the Greater Angle Is Greater Than the Side Opposite to Smaller Angle

For the trian...

Question

For the triangle below, which option correctly gives an arrangement of its sides in ascending order of their lengths?

AB, BC, CA

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AB, CA, BC

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AC, AB, BC

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CA, BC, AB

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Solution

The correct option is A
AB, BC, CA

In any triangle, the side opposite to the larger (greater) angle is longer.
The ascending order of the angles is $40^{\circ}, 65^{\circ}, 75^{\circ}$ .
So sides in ascending order will be AB, BC, AC.

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Similar questions

\vec{A B} + \vec{B C} + \vec{C A} = \vec{0}

\vec{A B} + \vec{B C} - \vec{A C} = \vec{0}

\vec{A B} + \vec{B C} - \vec{C A} = \vec{0}

\vec{A B} - \vec{C B} + \vec{C A} = \vec{0}

In Triangle ABC, which of the following is not true:

(a) AB + BC + CA = 0
(b) AB + BC - AC = 0
(c) AB + BC - CA = 0
(d) AB - CB + CA = 0

(a b + b c) (a b - b c) + (b c + c a) (b c - a c) + (c a + a b) (a c - a b)

A B C

- - \to A B + - - \to B C + - - \to C A = \to 0

- - \to A B + - - \to B C - - - \to A C = \to 0

- - \to A B + - - \to B C + - - \to A C = \to 0

- - \to A B - - - \to C B + - - \to C A = \to 0

(a b + b c) (a b - b c) + (b c + c a) (b c - a c) + (c a + a b) (a c - a b)

[3 M a r k s]

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