Question

The elevation of a tower from two points, one due east of the tower and the other due west of it are 20◦ and 24◦, respectively, and the two points of observation are 300 m apart. Find the height of the tower to the nearest metre

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The height of the tower is $60m.$

Step-by-step explanation:

Elevation of a tower from two points are $20 ^\circ$ and $24 ^\circ$

Distance from two points are $300m.$

Find:

Find the height of the tower.

Solution:

Let $BC=x$

$CD=300-x$

In $\triangle ACD$

$tan20^\circ=\frac {AC}{CD}$

$AC=0.364 \times (300-x)\\AC=109.2-0.364x$                  ...... (i)

In $\triangle ABC$

$tan24^\circ=\frac {AC} {BC}$

$AC=0.445x$           ...... (ii)

Now, (i) and (ii)

$109.2-0.364x=0.445x\\109.2=0.445x+0.364x\\109.2=0.809x\\x=134.9$

Putting eqn. (ii)

$AC=134.9 \times 0.445\\=60m$

Hence, the height of the tower is $60m.$

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