Given that angles A and B are complementary and cosA = 5/13, what is tanB?

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Accepted Answer

1. **Relation:** Angles A and B are complementary, so $	an B=\cot A=\dfrac{1}{	an A}$.  
2. **Find sin A:** From $\cos A=\dfrac{5}{13}$, we get $\sin A=\sqrt{1-\left(\dfrac{5}{13}ight)^2}=\dfrac{12}{13}$.  
3. **Find tan A:** $	an A=\dfrac{\sin A}{\cos A}=\dfrac{12/13}{5/13}=\dfrac{12}{5}$.  
4. **Compute tan B:** $	an B=\dfrac{1}{	an A}=\dfrac{5}{12}$.

FINAL_ANSWER: b

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