Question

Height of PQ=18mHeight of RS=???Length of QS= 25mThe angle of elevation of R from P is 32°Calculate the height in m of RS.A. 4.38B. 15.62C. 33.62D. 40.00

Answer 1

For the given diagram, we will find the length of RS

We will modify the diagram, it will be as shown in the following figure:

PO is parallel to QS, and equal in length to it

The angle of elevation of R from P is 32°

so, the measure of angle (OPR) = 32°

For the triangle OPR:

It is a right triangle at O

OP = 25 m

m∠OPR = 32°

So,

$\begin{gathered} \tan (\text{OPR)}=\frac{opposite}{adjacent}=\frac{OR}{OP} \\ \tan 32=\frac{OR}{25} \\ \\ OR=25\cdot\tan 32 \end{gathered}$

The length of RS = OR + OS

OS = QP = 18 m

so,

$\begin{gathered} RS=18+25\cdot\tan 32=18+15.62 \\ \\ RS=33.62m \end{gathered}$

So, the answer will be option C. 33.62