Question

10 If cos A=4/5 then the value of tan A is-
a ) 3/5
b ) 3/4
c ) 4/3
d )5/3​

Answer 1

Given:-

• $\sf{CosA = \dfrac{4}{5}}$

To find:-

• The value of TanA

Solution:-

$\sf{CosA = \dfrac{4}{5} = \dfrac{Base}{Hypotenuse}}$

Therefore,

Base = 4 units

Hypotenuse = 5 units.

According to Pythagoras Theorem

$\sf{{(Hypotenuse)}^{2} = {(Perpendicular)}^{2} + {(Base)}^{2}}$

=> $\sf{{(Perpendicular)}^{2} = {(Hypotenuse)}^{2} - {(Base)}^{2}}$

=> $\sf{Perpendicular = \sqrt{{(Hypotenuse)}^{2} - {(Base)}^{2}}}$

=> $\sf{Perpendicular = \sqrt{{(5)}^{2} - {(4)}^{2}}}$

=> $\sf{Perpendicular = \sqrt{25 - 16}}$

=> $\sf{Perpendicular = \sqrt{9}}$

=> $\sf{Perpendicular = 3\: units}$

Now,

$\sf{TanA = \dfrac{Perpendicular}{Base}}$

= $\sf{TanA = \dfrac{3}{4}}$

$\sf{The\: value\: of\: TanA\: is \dfrac{3}{4}}$

Some important Points:-

• $\sf{SinA = \dfrac{Perpendicular}{Hypotenuse}}$

• $\sf{CosA = \dfrac{Base}{Hypotenuse}}$

• $\sf{TanA = \dfrac{Perpendicular}{Base}}$

• $\sf{CosecA = \dfrac{Hypotenuse}{Perpendicular}}$

• $\sf{SecA = \dfrac{Hypotenuse}{Base}}$

• $\sf{CotA = \dfrac{Base}{Perpendicular}}$