Question

If cos A = 1 / 3 find the value tan A
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Answer 1

$\purple{\bf {\underline {Solution:-}}}$

$\tt{cosA} = \frac{1}{3}$

So, in the triangle,

• Hypotenuse = 3
• Base = 1

We have to find, the value of Perpendicular.

We know from Pythagoras formula,

$\red{\tt{Hypotenuse^{2} = {Perpendicular }^{2} + {Base}^{2} }}$

${ \tt{⟹ {3}^{2} =Perpendicular^{2} + {1}^{2} }}$

${ \tt{⟹9 = {Perpendicular}^{2} + 1 }}$

${ \tt{⟹9 - 1 = {Perpendicular}^{2} }}$

${ \tt{⟹Perpendicular^{2} = 8}}$

$\tt{⟹Perpendicular = \sqrt{8} }$

• $\pink{\tt{Hence, The \: value \: of \: tanA = \frac{ \sqrt{8} }{1} = \sqrt{8} }}$