Question

if cos theta is 24/25,where theta is an acute angle.find the value of sin theta
​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \cos \theta = \frac{24}{25} }$

Where θ is an acute angle

TO DETERMINE

The value of sin θ

EVALUATION

Here it is given that

$\displaystyle \sf{ \cos \theta = \frac{24}{25} }$

Squaring both sides we get

$\displaystyle \sf{ {\cos}^{2} \theta = \frac{576}{625} }$

$\displaystyle \sf{ \implies 1 - {\cos}^{2} \theta =1 - \frac{576}{625} }$

$\displaystyle \sf{ \implies {\sin}^{2} \theta = \frac{625 - 576}{625} }$

$\displaystyle \sf{ \implies {\sin}^{2} \theta = \frac{49}{625} }$

$\displaystyle \sf{ \implies {\sin}^{} \theta = \frac{7}{25} }$

FINAL ANSWER

$\boxed{ \: \: \displaystyle \sf{ {\sin}^{} \theta = \frac{7}{25} \: \: }}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

2. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

3. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971