Question

The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. Use`[sqrt3=1.732]`

Answer 1

Let AB and CD be two poles, where CD = 24 m.

It is given that angle of depression of the top of the pole AB as seen from the top of the pole CD is 30° and horizontal distance between the two poles is 15 m.

∴ ∠CAL = 30° and BD = 15 m.

To find: Height of pole AB

Let the height of pole AB be h m.

AL = BD = 15 m and AB = LD = h

Therefore, CL = CD − LD = 24 − h

Consider right ΔACL:

`tan angleCAL =\text{perpendicular}/\text{Base}=(CL)/(AL)`

`rArrtan 30^o=(24-h)/15`

`rArr 24-h=15/sqrt3`

`rArr24-h=5sqrt3`

`rArrh=24-5sqrt3`

`rArrh=24-5xx1.732` `[\text{Taking}sqrt3=1.732]`

`rArrh=15.34`

Therefore, height of the pole AB = h m = 15.34 m.