A building and a statue are in opposite side of a street from each other $35 \; m$ apart. From a point on the roof of the building, the angle of elevation of the top of statue is $24^\circ$ and the angle of depression of the base of the statue is $34^\circ$. Find the height of the statue. Give your answer correct to two decimal places. [Given: $\tan 24^\circ = 0.4452$, $\tan 34^\circ = 0.6745$]
$AB =$ Building
$ST =$ Statue
$AS = 35 \; m = $ Distance between the building and the statue
Draw $BO \perp ST$.
Then, $\;$ $AB = SO$, $\;$ $AS = BO = 35 \; m$
In $\triangle ABS$, $\;$ $\dfrac{AB}{AS} = \tan 34^\circ$
$\implies$ $AB = AS \tan 34^\circ = 35 \times 0.6745 = 23.6075 \; m$
i.e. $\;$ $SO = 23.6075 \; m$
In $\triangle BTO$, $\;$ $\dfrac{OT}{BO} = \tan 24^\circ$
$\implies$ $OT = BO \tan 24^\circ = 35 \times 0.4452 = 15.582 \; m$
Now, $\;$ $ST = SO + OT = 23.6075 + 15.582 = 39.1895 \; m$
$\therefore \;$ The height of the statue $= 39.19 \; m$ (to 2 decimal places)