Question

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

Answer 1

$\Rightarrow PQ=5cm$

$\Rightarrow PR+QR=25cm$

$\Rightarrow PR=25-QR$

Now, In $△PQR$

$\Rightarrow {\left(PR\right)}^2=P{Q}^2+Q{R}^2$

$\Rightarrow {(25-QR)}^2=5^2+Q{R}^2$

$\Rightarrow 625+Q{R}^2-50QR=25+Q{R}^2$

$\Rightarrow 50QR=600$

$\Rightarrow QR=12cm$

$\Rightarrow PR=25-12=13cm$

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

Hence, the answers are $\sin P=\frac{12}{13},\cos P=\frac{5}{13},\tan P=\frac{12}{5}.$