Question

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

Answer 1

In $\Delta$ OPQ, we have

$O{Q}^2=O{P}^2+P{Q}^2$
$\Rightarrow (PQ+1{)}^2=O{P}^2+P{Q}^2[\because OQ-PQ=1\Rightarrow OQ=1+PQ]$

$\Rightarrow P{Q}^2+2PQ+1=O{P}^2+P{Q}^2$
$\Rightarrow 2PQ+1=49$
$\Rightarrow PQ=24cm$

$\therefore OQ-PQ=1cm$
$\Rightarrow OQ=(PQ+1)cm=25cm$

Now, $sinQ=\frac{OP}{OQ}=\frac{7}{25}$
and, $cosQ=\frac{PQ}{OQ}=\frac{24}{25}$