Question

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

Answer 1

$OQ-PQ=1$

$\Rightarrow OQ=1+PQ$

In $\Delta OPQ$

$\Rightarrow O{Q}^2=O{P}^2+P{Q}^2$

$\Rightarrow (1+PQ{)}^2=O{P}^2+P{Q}^2$

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

$\Rightarrow 1+2PQ=49$

$\Rightarrow PQ=24$

$OQ=1+PQ=25$

$\sin \theta =\frac{OP}{OQ}=\frac{7}{25}$

$\cos \theta =\frac{PQ}{OQ}=\frac{24}{25}$.