Question

In the given figure, $tan{x}^o=\frac{4}{3}$ and "T" is the mid-point of PR, calculate the length of PQ.

• A. $\sqrt{8}$ m
• B. $9$ m
• C. $\sqrt{59}$ m
• D. $10$ m

Answer 1

The correct option is D $10$ m

In $△RST$

$\Rightarrow \tan x=\frac{RT}{SR}$

$\Rightarrow \frac{4}{3}=\frac{RT}{3}$

$\Rightarrow RT=4m$

$\therefore PR=2RT=8m$

Now, $△PSQ$ is a right angled triangle, such that

$\Rightarrow PQ{PR}^2+{PQ}^2={PQ}^2$

${\Rightarrow PQ}^2+{PR}^2={RQ}^2={\left(8\right)}^2+{\left(6\right)}^2=64+364$

$\Rightarrow PQ=\sqrt{100}=10m$

Hence, the answer is $10m.$