Question

If in a triangle ABC ,right angled at C ,tan B=12/5,then find sin B

Answer 1

The value of sin B is 12 / 13.

Given: If in a triangle ABC, right-angled at C, tan B = 12 / 5.

To Find: The value of sin B.

Solution:

• We know that in a right-angled triangle, there is a base, a perpendicular, and a hypotenuse concerning the angle which is equal to 90°.

• Accordingly, we can say that;

            tan A = Perpendicular / Base                                          ...(1)

             sin A = Perpendicular / Hypotenuse                             ...(2)

            cos A = Base / Hypotenuse                                            ...(3)

• The Pythagoras theorem states that;

            ( Hypotenuse )² = ( Perpendicular )² + ( Base )²             ...(4)

Coming to the numerical, we are given;

Δ ABC is right-angled at C,

             tan B = 12 / 5 = Perpendicular / Base

So, we can say that,

The perpendicular concerning ∠B = 12 units

The base concerning ∠B = 5 units

So, we can find the hypotenuse from (4),

              ( Hypotenuse )² = ( Perpendicular )² + ( Base )²    

          ⇒ ( Hypotenuse )² = ( 12 )² + ( 5 )²    

          ⇒ ( Hypotenuse )² = 144 + 25

          ⇒ ( Hypotenuse ) = √169

                                        = 13 units

So, we need to find the sine of ∠B. So, we put the respective values in (2);

                 sin B = Perpendicular / Hypotenuse      

             ⇒  sin B = 12 / 13

Hence, the value of sin B is 12 / 13.

#SPJ2    

Answer 2

Answer:

sin B = 12/13

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