# 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. - Geometry

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.

• 30°

• 60°

• 90°

• 45°

#### Solution

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

AB2 =  (6sqrt(3))2 = 108
AC2 = (12)2 = 144
BC2 = (6)2 = 36
108 + 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°
Concept: Apollonius Theorem
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#### APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 2 Pythagoras Theorem
Problem Set 2 | Q 1.8 | Page 43