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In triangle ABC, hypotenuse $A C = 16 cm$ and $∠ A = 60 °$ then what will be the length of the remaining sides?

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x = 83 c m, y = 8 c m

x = 62 c m, y = 6 c m

x = 63 c m, y = 6 c m

x = 63 c m, y = 8 c m

answer is A.

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Detailed Solution

Given that,
The hypotenuse

A C = 16

∠ A = 60 °

We use the trigonometric identities,

sin θ = p e r p e n d i c u l a r h y p o t e n u s e

cos θ = b a s e h y p o t e n u s e

The diagram will be,
Question Image

Taking

A B = y

The perpendicular

B C = x

Using the trigonometric identities,

⇒ sin A = x A C ⇒ sin 60 ° = x 16 ⇒ 32 = x 16 [∵ sin 60 ° = 32] ⇒ x = 83 cm

Using the trigonometric identities to get the length of the base,

⇒ cos A = y A C ⇒ cos 60 ° = y 16 ⇒ 12 = y 16 [∵ cos 60 ° = 12] ⇒ y = 8 cm

Thus the length of remaining sides of a triangle will be

x = 83 c m, y = 8 c m

.
Therefore the correct option is 1.

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