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  • If cos A = 4 by 5, then the value of tan A is (a)3 by 5 (b) 3 by 4 (c) 4 by 3 (d) 5 by 3

If cos A =4/5, then the value of tan A is

(a) \frac{3}{5}                    (b)  \frac{3}{4}                    (c)  \frac{4}{3}                     (d)  \frac{5}{3}

Answers (1)

It is given that cos A = 4/5
\text{We know that cos}\theta=\frac{Base}{Hypotenuse}  
 \therefore value of base = 4
  Hypotenuse = 5

Use Pythagoras' theorem in \bigtriangleupABC
(Hypotenuse)2 = (Base)2 + (perpendicular)
\left ( AC \right )^{2}= \left ( BC \right )^{2}+\left ( AB \right )^{2}
\left ( 5 \right )^{2}= \left ( 4 \right )^{2}+\left ( AB \right )^{2}
25-16= \left ( AB \right )^{2}
9= \left ( AB \right )^{2}
\sqrt{9}= AB
3= AB
That is the value of the perpendicular is 3
\text{Also we know that tan}\theta=\frac{perpendicular}{base}  

 \therefore \tan \, A= \frac{3}{4}
Hence option (B) is correct.

Posted by

infoexpert27

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