Question

The angles shown above are acute and $\sin \left(a^{\circ }\right)=\cos b^{\circ }$. If $a=4k-22$ and $b=6k-13$, what is the value of $k$?

• A. $4.5$
• B. $5.4$
• C. $12.5$
• D. $21.5$

Answer 1

The correct option is C $12.5$

Given: $\sin \left(a^o\right)=\cos \left(b^o\right)$

$\Rightarrow \sin \left(a^o\right)=\sin ({90}^o-b^o)$

$\Rightarrow a^o={90}^o-b^o$

$\Rightarrow a^o+b^o={90}^o$

$\Rightarrow 4k-22+6k-13=90$

$\Rightarrow 10k=90+35$

$\Rightarrow 10k=125$

$\Rightarrow k=12.5$

Hence, option C is correct.