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In a right-angled triangle $Δ A B C$ such that $∠ B = 90 °,$ if $A B = 5 cm$ and $B C = 12 cm,$ then which of the following is the value of $sin A$ ?

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53

1213

713

73

answer is B.

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Detailed Solution

Given that

Δ A B C

is a right-angled triangle at B such that

A B = 5 cm

and

B C = 12 cm .

In a right angle triangle ABC rightangled at B if -class-11-maths-CBSE

Using Pythagoras theorem, we have,

A C 2 = A B 2 + B C 2 ⇒ A C 2 = 52 + 122 ⇒ A C 2 = 169 ⇒ A C = 13

Using the definition of trigonometric ratio, we have,

sin A = P H ⇒ sin A = 1213

Therefore, the value of

sin A = 1213 .

Hence, option (2) is correct.

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