Question

If cos $\theta$ = $\frac{4}{5}$ then tan $\theta$ = ?

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

Answer 1

$cos\theta =\frac{4}{5}$

But $cos\theta =\frac{Adjacentside}{Hypotenuseside}$

Hypotenuse = 5

Adjacent side = 4

According to Pythagoras theorem,

$(\text{Hypotenuse}{)}^2=(\text{Base}{)}^2+\left(\text{Altitude}{)}^2\right(\text{Altitude}{)}^2=(\text{Hypotenuse}{)}^2-(\text{Base}{)}^2(\text{Altitude}{)}^2=5^2-4^2=25-16(\text{Altitude}{)}^2=9\text{Altitude}=3$

$tan\theta =\frac{Oppositeside}{Adjacentside}=\frac{3}{4}$