#### Question

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°

#### 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°

Is there an error in this question or solution?

Solution Some Question and Their Alternative Answer Are Given. Select the Correct Alternative. in ∆Abc, Ab = 6 √ 3 Cm, Ac = 12 Cm, Bc = 6 Cm. Find Measure of ∠A. Concept: Apollonius Theorem.