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

 Dec 1, 2020
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B

            5

 

A                    C

 

 

tan B  = 2  means  that     AC/ BA =  2

So  AC  must be twice as long as  BA

 

Let  AB = x     so  AC  = 2x

 

And using the Pythagorean Theorem

 

x^2  + (2x)^2  = 5^2

 

5x^2  = 25

 

x^2  = 5

 

x = sqrt (5) =  AB

 

 

cool cool cool

 Dec 1, 2020

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