Question

In $\Delta$ PQR, right angled at Q, $PQ=4$ cm and $QR=3$ cm. Find the value of $\sin P,\sin R,\sec P$ and $\sec R$.

Answer 1

Consider the figure above,

From Pythagoras theorem,

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

$P{R}^2=4^2+3^2$

$P{R}^2=16+9=25$

$PR=5$

We know that,

$\cos \theta =\frac{adjacentSide}{Hypotenuse}$

$\cos P=\frac{QP}{RP}=\frac{4}{5}$

$\sec P=\frac{1}{\cos P}=\frac{RP}{QP}=\frac{5}{4}$

$\cos R=\frac{QR}{RP}=\frac{3}{5}$

$\sec R=\frac{1}{\cos P}=\frac{RP}{QR}=\frac{5}{3}$

We know that,

$\sin \theta =\frac{oppositeSide}{Hypotenuse}$

$\sin P=\frac{QR}{RP}=\frac{3}{5}$

$\sin R=\frac{PQ}{RP}=\frac{4}{5}$