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In triangle BCD, angle C = 90 degrees, CD = 3, and BD = sqrt(14) . What is tan B?

 May 1, 2022
 #1
avatar+124598 
+1

B

 

                sqrt 14              

 

C       3             D

 

BC =  sqrt [ (sqrt 14)^2 - 3^2 ]   = sqrt  5

 

tan B  =   CD  /   BC  =     3 /  sqrt 5  =   3sqrt (5)  /  3

 

cool cool cool

 May 1, 2022
 #2
avatar+2455 
0

By the Pythagorean Theorem, \(BC= \sqrt 5 \)

 

Because \(\tan = { \text{opposite} \over \text{adjacent}}\)\(\tan B = {3 \over \sqrt 5 }\), which can be rationalized to \(\color{brown}\boxed{3 \sqrt 5 \over 5}\)

 May 2, 2022

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