Question

In $\Delta OPQ$, right angled at $P,OP=7cm$ and $OQ-PQ=1cm$. Determine the values of $\sin Q$ and $\cos Q$

Answer 1

Let $PQ=x$

$OQ=x+1$

$(PQ-OQ=-1)$

${\left(OP\right)}^2+{\left(PQ\right)}^2={\left(OQ\right)}^2$

$x^2+49={(x+1)}^2$

$x^2+49=x^2+1+2x$

$48=2x\Rightarrow x=24$

$\therefore PQ=24$ and $OQ=25$

$\sin \theta =\frac{OP}{OQ}=\frac{7}{25}$, and $\cos \theta =\frac{QP}{OQ}=\frac{24}{25}$