Question

In above figure, if $PS=14cm,$ then 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 $\frac{4}{3}$

From the figure in the question,

As $PQRT$ is a parallelogram

$QR=PT=5cm$

Given, $PS=14cm$

$PS=PT+TS$

$\Rightarrow 14=5+TS$

$\therefore TS=9cm$

From $△PQR;$ By Pythogoras Theorem

${PQ}^2={PR}^2={QR}^2$

$PQ=\sqrt{{13}^2-5^2}=12cm$

$\Rightarrow PQ=TR=12cm$ [opposite of parallelogram are equal]

$\therefore$ from $△STR$

$\tan a=\frac{12}{9}=\frac{4}{3}$