In ∆ABC, AB = [6sqrt{3}] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
30°
60°
90°
45°
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.8 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
In ∆ABC, AB = [6sqrt{3}] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
30°
60°
90°
45°
solution
In ∆ABC, AB = [6sqrt{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°
Explanation:- We can solve this problem using the cosine rule, which states that in a triangle with sides of lengths a, b, and c and angle A opposite side a,
cos A = (b² + c² – a²) / 2bc
Applying this formula to ∆ABC with angle A opposite side BC, we have:
cos A = (6² + 12² – ([6sqrt{3}])²) / (2 × 6 × 12) cos A = (36 + 144 – 108) / 144 cos A = 72 / 144 cos A = 1 / 2
Using a calculator or reference table, we find that cos 60° = 1 / 2, so we have:
A = 60°
Therefore, the correct answer is (B) 60°.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.8 | Page 44