Question

A man, $1.7$ metres tall, standing at the foot of a tower sees the top of a building $50$ metres away at an angle of elevation ${60}^o$. On climbing the top of the tower, he sees it at an angle of elevation of ${50}^o$.
Draw a rough figure according to the given data. Compute the height of the tower and the building.
$(\sin {50}^o=0.77,\cos {50}^o=0.64,\tan {50}^o=1.19)(\sin {60}^o=0.87,\cos {60}^o=0.50,\tan {60}^o=1.73)$

Answer 1

Given that, a man, $1.7m$ tall, standing at the foot of a tower sees the top of building that is $50m$ away from the foot of the tower. The angle of elevation is ${60}^o$. On climbing the tower, he sees the angle of elevation as ${50}^o$.

To find out: The height of the tower.

On the basis of the given information, we can drawn the figure shown above.

Here,

Height of the building $=PQ$
Height of the tower $=AC$
The distance between the building and the tower, $AP=50m$

From the right $△BRQ$,
$RQ=BR\times \tan {60}^o=50\times 1.73=86.5$
$PQ=PR+RQ=1.7+86.5=88.2$
Thus, the height of the builiding is about $88.2m$.

From right $△DTQ$,
$QT=DT\times \tan {50}^o=50\times 1.19=59.5$
$AC=PS=PQ(QT+TS)$
$\Rightarrow$ $AC=88.2-(59.5+1.7)$
$\Rightarrow$ $AC=88.2-61.2=27m$

Hence, the height of the tower is about $27m$.