Question

If cos A=12/13,then find sin A and tan A










​

Answer 1

Answer:

=0.417

Step-by-step explanation:

Correct option is A)

cosA=

13

12

​

               ---- ( 1 )

We know,

sin

2

A+cos

2

A=1

⇒  sin

2

A+(

13

12

​

)

2

=1                     [ From ( 1 ) ]

⇒  sin

2

A+

169

144

​

=1

⇒  sin

2

A=1−

169

144

​

⇒  sin

2

A=

169

169−144

​

⇒  sin

2

A=

169

25

​

⇒  sinA=

13

5

​

                    ----- ( 2 )

Now,

tanA=

cosA

sinA

​

⇒  tanA=

13

12

​

13

5

​

​

                         [ From ( 1 ) and ( 2 ) ]

⇒  tanA=

12

5

​

∴  sinA=

13

5

​

=0.385

∴  tanA=

12

5

​

=0.417

Answer 2

Hey dear here is your answer

It is given that ,

$\: cos \: A = \frac{adjacent \: side}{hypotenuse } \\ \frac{12}{13}$

Calculate the opposite side of the triangle as shown,

$opposite \: side = \sqrt{ {(hypotenuse)}^{2} } - {(adjacent \: side )}^{2} \\ = \sqrt{ {13}^{2} - {12}^{2} } \\ = \sqrt{169 - 144} \\ = \sqrt{25} \\ = 5 \: units$

Calculate the value of sin A as shown,

$sin \: A = \frac{opposite \: side \: }{hypotenuse} \\ = \frac{5}{13}$

Calculate the value of tan A as shown,

$tan \: A = \frac{opposite \: \: side}{adjacent \: side \: } \\ = \frac{5}{12}$

Final Answer

$the \: value \: of \: sin \: A \: = \frac{5}{13} \\ \\ the \: value \: of \: tan \: A = \frac{5}{12}$

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