Question

In above fig.1, triangle PQR & STR are right-angle triangles. If PS $=$ 14 cm, the value of $\tan a$ is equal to :

• A. $\frac{4}{3}$
• B. $\frac{14}{3}$
• C. $\frac{5}{3}$
• D. $\frac{13}{3}$

Answer 1

The correct option is A $\frac{4}{3}$

Using Pythagoras theorem for $△PQR$ ,

$P{Q}^2+{QR}^2={PR}^{2}P{Q}^2+5^2={13}^2\Rightarrow P{Q}^2=144\Rightarrow PQ=12cm$

$TR=PQ$ and $PT=QR$ ------(From figure i.e, sides of the rectangle)

$\Rightarrow TR=12cmPS=PT+TS14=5+TS\Rightarrow TS=9cm\tan a=\frac{TR}{TS}=\frac{12}{9}=\frac{4}{3}$