MCQ

Some question and their alternative answer are given. Select the correct alternative.

In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.

#### Options

30°

60°

90°

45°

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#### Solution

In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm.

AB

AC

BC

^{2}= `(6sqrt(3))`^{2}= 108AC

^{2}= (12)^{2}= 144BC

^{2}= (6)^{2}= 36108 + 36 = 144

In a triangle, if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle.

In a right angled triangle, if one side is half of the hypotenuse then the angle opposite to that side is 30°.

Here, BC is half of AC.

Thus, measure of ∠A is 30°

Hence, the correct option is 30°

In a triangle, if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle.

In a right angled triangle, if one side is half of the hypotenuse then the angle opposite to that side is 30°.

Here, BC is half of AC.

Thus, measure of ∠A is 30°

Hence, the correct option is 30°

Concept: Apollonius Theorem

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