Question

If in the $\Delta PQR,\angle Q={90}^o,PQ=4cm$ and $PR=9cm$ then find the values of the following:

i) $\sin P$

ii) $\cos P$

iii) $\tan R$

iv) $\sin R+\cos R$.

Answer 1

$\angle Q={90}^o$,

$PQ=4$cm

$PR=9$cm

By Pythagoras theorem

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

$9^2=4^2+Q{R}^2$

$36-16=Q{R}^2$

$20=Q{R}^2$

$QR=\sqrt{20}=2\sqrt{5}=4.47$

$\sin P=\frac{QR}{PR}=\frac{2\sqrt{5}}{9}$

$\cos P=\frac{QP}{PR}=\frac{4}{9}$

$\tan R=\sin R/\cos R$

$=PQ/QR$

$=\frac{4}{2\sqrt{5}}=\frac{2}{\sqrt{5}}$

$\sin R+\cos R=\frac{PQ}{PR}+\frac{QR}{PR}$

$=\frac{4}{9}+\frac{2\sqrt{5}}{9}$

$=\frac{4+2\sqrt{5}}{9}$.