Question

If sin $(\theta +{36}^{\circ })=cos\theta$, where $\theta$ and $\theta +{36}^{\circ }$ are acute angles, then the value of $\theta$ is

• A. ${36}^{\circ }$
• B. ${54}^{\circ }$
• C. ${27}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (C)

${27}^{\circ }$

$\sin (\theta +36°)=\cos \theta$

$\Rightarrow \sin (\theta +36°)=\sin (90°-\theta )$

$\Rightarrow \theta +36°=90°-\theta$

$\Rightarrow 2\theta =54$

$\Rightarrow \theta =27°$

Hence, the answer is $27°.$