Question

Choose the correct option for the following.

If $\sin \theta =\frac{5}{13}$, then $\cos \theta =\frac{12}{13}$.

• A. True
• B. False
• C. ambiguous
• D. Data insufficient

Answer 1

The correct option is A True

Given,

$\sin \theta =\frac{5}{13}$

$\sin \theta =\frac{P}{H}=\frac{5}{13}$

$P=5$, $H=13$

Thus, by Pythagoras Theorem,

$H^2=B^2+P^2$

${13}^2=5^2+B^2$

$B^2=144$

$B=12$ cm

$\cos \theta =\frac{B}{H}=\frac{12}{13}$