Question

if sin teeta = 1/3 , then tan teeta =
______

options:

a) 2 root 2
b) 1/2
c)1/2 root 2
d) 1/root 3

correct answer is 1/ 2 root 2
but I want steps If anyone answers with steps I will make them brainliest. ​

Answer 1

★ Correct diagram

$\setlength{\unitlength} {1mm}\begin{picture} (5,5)\put(0,0){\line(1,0) {30}}\put(30,0){\line(0,1) {40}}\put(0,0){\line(3,4) {30}}\put(13,-4){2.28} \put(32,17){1}\put(8,23) {3 }\put(3,1){ \theta } \end{picture}$

★ Given:

• sin$\sf\theta=\dfrac{1}{3}$

★ To find:

• tan$\theta$

★ Solution:

Given,

sin$\sf\theta=\dfrac{1}{3}$

That means

Opposite side of $\theta$ = 1

Hypotenuse of given ∆ = 3

Now, finding adjacent side of $\theta$ by Pythagoras theorem

(Hypotenuse)$^2$ = Base$^2$ + Height$^2$

$\longrightarrow$ 3² = 1² + Height²

$\longrightarrow$ 9 - 1 = Height ²

$\longrightarrow$ Height = $\sqrt{8}$

$\longrightarrow$ Height = 2 $\bf \sqrt2$

$\rule{200}3$

Now, finding tan$\theta$

$\diamond$ tan$\theta$ = $\bf\dfrac{opposite}{adjacent}$

$\diamond$ tan$\theta$ = $\dfrac{1}{2\sqrt2}$

Hence, tan$\theta$ = $\bf\dfrac{1}{2\sqrt2}$