Q. 16 A3.7( 3 Votes )

# In ΔABC, if AB = (2a-1)cm. AC = 2 √2acm. And BC = (2a + 1)cm., then let us write the value of ∠BAC.

Answer :

Let’s consider that the triangle is a right angled triangle,

By applying Pythagoras theorem we get,

(2a + 1)^{2} = (2√2a)^{2} + (2a-1)^{2}

⇒ (2a)^{2} + 1^{2} + 2×2a×1 = 4×2a + (2a)^{2} + 1^{2} - 2×2a×1

⇒ 4a^{2} + 1 + 4a = 8a + 4a^{2} + 1 - 4a

⇒ 4a^{2} + 1 + 4a = 4a^{2} + 1 + 4a

Since, the sides of the triangle satisfy Pythagoras theorem, thus the triangle is a right angled triangle with angle opposite to hypotenuse as right angle.

Here,

H = 2a + 1

P = 2a-1

B = 2√2a

Thus, ∠BAC is a right angle with measure 90°.

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