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In right triangle ABC, we have ∠A = 90◦ , tan B = 5, and BC = 2. What is the length of AB?

 Jun 24, 2022
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B

 

              2

 

A                   C

 

If tan B  = 5.....then  the ratio of AC / BA =  5/1  ....so  ....   AC = 5BA 

 

Using the Pythagorean Theorem

 

BA^2 + AC^2=  BC^2

 

BA^2  +  (5 BA)^2 =  2^2

 

BA^2  + 25 BA^2   =  4

 

 

26 BA^2 =  4

 

BA^2  = 4 /26  =  2 /13

 

BA  = sqrt  (2/13) =   2sqrt (13) / 13  ≈  .392

 

 

cool cool cool

 Jun 24, 2022

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