Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. tan ⁡ ( A ) = 5 12 , b = 2 a = ? c = ?

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Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.  tan  ⁡  (  A  )  =      5    12    ,  b  =  2  a  =  ?  c  =  ?

coolng90qo · Accepted Answer

Step 1Given   tan  ⁡  (  A  )  =      5    12    ,  b  =  2But from triangle ABC  tan  ⁡  A  =      a    b    ⇒      5    12    =      a    b      ⇒      5    12    =      a    2      ⇒  a  =      5    12    ×  2  =      5    6      a  =      5    6  Step 2We know that pythagorus theorem      c    2    =      a    2    +      b    2          c    2    =  (      5    6        )    2    +  (  2      )    2      c  =            25      36        +  4    c  =            169      36          c  =      13    6

Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. tan (A)=5/12, b=2

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