Question

In a rectangle ABCD, AB = 20 cm, ∠BAC= 60°, calculate side BC and diagonals AC and BD.

Answer 1

BC = 20√3 cm

AC=BD= 40 cm

In triangle ABC

<B is right angle

=>cos 60°= B/H= AB/AC

=>1/2=20/AC

=>AC= 40 cm

=> BD = 40 cm ( diagonals of

rectangle are equal)

also tan 60° = P/B =BC/AB

=> √3 = BC/20

=> BC = 20√3 cm

Answer 2

Value of diagonal AC =BD =40 cm  and $\mathbf{BC=20\sqrt{3} \ cm}$

Step-by-step explanation:

• Given data

        AB = 20 cm

        ∠BAC= 60°

• From trigonometry relation

        $\mathbf{\tan 60^{\circ}=\frac{BC}{AB}}$

        So

        $\mathbf{BC=AB\times \tan 60^{\circ} =20\sqrt{3} \ cm}$

• From trigonometry relation

        $\mathbf{\cos 60^{\circ}=\frac{AB}{AC}}$

        $\mathbf{AC=\frac{AB}{\cos 60^{\circ}}}$

        $\mathbf{AC=\frac{20}{\frac{1}{2}}=40 \ cm}$

• So value of diagonal AC =BD =40 cm  and $\mathbf{BC=20\sqrt{3} \ cm}$