Question

IN MEASURE ANGLE ABC MEASURE ANGLE B=90 DEGREE MEASURE ANGLE C=MEASURE ANGLE A=45 . IF AB=6 THEN AC​

Answer 1

Given :-

• ∠B = 90°
• ∠C = ∠A = 45°
• AB = 6 cm

To find :-

• Length of AC = ?

Solution:-

Let side AC be x.

We know that side opposite to equal angle is equal.

So,

⟹ ∠C = ∠A

⟹ AB = BC

⟹ BC = 6 cm ( because AB is also 6 cm.)

So, by Pythagoras Theorem which is applied on the Triangle ABC which is Right Angled Triangle :-

⟹ AC² =BC² +AB²

⟹ AC² = (6)² + (6)²

⟹ (AC)² = 36 + 36

⟹ AC² = 72

⟹ AC = √72

⟹ AC = 8.48 cm

So, length of AC is 8.48 cm.

Answer 2

Given :

• $\sf Right\: triangle \:ABC$
• $\sf \angle ABC\:=\: 90°$
• $\sf \angle BAC\:=\: \angle BCA\:=\:45°$
• $\sf Side AB \:=\: 6\:cm$

To Find :

• $\sf Side\: AC$

Solution :

• As we know that side opposite to equal angles of a triangle are equal therefore , AB = AC = 6 cm

• Using pythagoras theorem :

$\star \: {\sf{\red{Hypotenuse²\:=\:Perpendicular²\:+\:Base²}}}$

$\implies \sf AC²\:=\: 6²\:+\:6²$

$\implies \sf AC²\:=\: 36\:+\:36$

$\implies \sf AC²\:=\: 72$

$\implies \sf AC\:=\: \sqrt{72}$

$\implies \sf AC\:=\:8.48\:cm$

• Side AC = 8.48 cm

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