Question

In $△PQR$ right angled at $Q,PR+QR=25cm$ and $PQ=5cm$. Determine the values of $\sin P,\cos P$ and $\tan P$.

Answer 1

$PR+QR=25....\left(1\right),PQ=5$

By Pythagorus theorem,

$P{Q}^2+Q{R}^2=P{R}^2$

$\Rightarrow 25=P{R}^2-Q{R}^2$

$\Rightarrow PR-QR=1$ ………..$\left(2\right)$

$\left(1\right)+\left(2\right)$

$\Rightarrow 2PR=26$

$\Rightarrow PR=13$ and $QR=12$

$\Rightarrow \sin P=\frac{QR}{PR}=\frac{12}{13}$

$\cos P=\frac{PQ}{PR}=\frac{5}{13}$, $\tan P=\frac{\sin P}{\cos P}=\frac{12}{5}$.