## anonymous one year ago From the top of a cliff,60 metres high, the angles of depression of the top and bottom of a tower are observed to be 30 ° and 60 °.Find the height of the tower.

1. anonymous

I can't understand..

2. UnkleRhaukus

$\tan\theta = \frac{\text{opp}}{\text{adj}}$

Let AB be the building h meters high, and PQ be the tower 60 m high situated at distance BQ = x meters away. Then AC = BQ = x, CQ = AB = h, PC = 60 -h From BPQ, cot 60° = BQ/PQ = x/60 => x = 60 cot 60° From APC, cot 30° = AC/PC = x/(60 -h) => 60 -h = x/ cot 30° = 60 cot 60° tan 30° = 60 (1/3)(1/3) = 20 => h = 60 -20 = 40 Thus the building is 40 meters high and is situated 34·64 meters away from the tower.

i've given you the figure pls refer to it

6. sepeario

^^^^ i think the use of inverse trigonometric functions is unnecessary.

no by cot theta it is helpful and cot theta is just the opposite of tan theta

8. sepeario

Yes, but I don't think this person has actually learnt inverse trigonometry, and for the sake of simplicity I don't think he/she needs to know it for now.