Question

8. sin=1/2 then find the value of tana​

Answer 1

Correct Question:-

• Sin $\dfrac{1}{2}$ then find the value of tan .?

Given:-

$\implies \sf sin = \dfrac{1}{2}$

To find:-

$\dashrightarrow$ The value of tan.

How to find?

• We have given the value of sin so sin = p/H so here base is not given .
• Now by using Pythagoras theroam firstly we will find base and then we will be with the answer.
• So Lets start

Solution:-

$\implies \sf sin = \dfrac{1}{2} = \dfrac{p}{h}$

So, here.

$\implies \sf Perpendicular = 1 \\ \implies \sf Hypotenuse = 2 \\ \implies \sf Base(?)$

Now,

According to Pythagoras formula.

$\large {\boxed {\boxed {\sf {\red { (H)^{2} = (P)^{2} + (B)^{2} }}}}}$

We will find the base,.

$\implies \sf (H)^{2} = (P)^{2} + (B)^{2} \\ \\ \implies \sf (2)^{2} = (1)^{2} + (B)^{2} \\ \\ \implies \sf 4 = 1 + (B)^{2} \\ \\ \implies \sf 4 - 1 = (B)^{2} \\ \\ \implies \sf 3 = (B)^{2} \\ \\ \implies \sf \sqrt{3} = B$

So by above solving we get the value of base .

$\hookrightarrow$We know that

$\sf tan = \dfrac{perpendicular}{Base}$

So now

$\implies \sf perpendicular= 1 \\ \\ \implies \sf Hypotenuse = 2 \\ \\ \implies \sf Base = \sqrt{3}$

Hence, $\hookrightarrow \sf tan = \dfrac{1}{\sqrt{3}}$

Answer:-

$\large {\boxed {\boxed {\sf {\red {Answer = \dfrac{1}{\sqrt{3}} }}}}}$

More to know:-

$\implies \sf sin = \dfrac{Opposite \: side }{Hypotenuse} = \dfrac{P}{H} \\ \\ \implies \sf cos = \dfrac{Adjacent\: side }{Hypotenuse} = \dfrac{B}{H} \\ \\ \implies \sf tan = \dfrac{Opposite\: side }{Adjacent\:side} = \dfrac{P}{B} \\ \\ \implies \sf cosec= \dfrac{Hypotenuse}{Opposite \:Side} = \dfrac{H}{P} \\ \\ \implies \sf Sec = \dfrac{Hypotenuse}{Adjacent \:Side} = \dfrac{H}{B} \\ \\ \implies \sf Cot = \dfrac{Adjacent\: side}{Opposite\: side} = \dfrac{B}{P}$