From-the-top-of-a-tower-80m-high-a-student-observe-that-the-angle-of-depression-of-the-top-of-a-vertical-pole-A-is-45-and-the-angle-of-depression-of-point-B-on-the-pole-is-60-if-O-is-the-foot-of

Question Number 9813 by tawakalitu last updated on 05/Jan/17

From the top of a tower 80 m high, a student

observe that the angle of depression of the top

of a vertical pole A is 45 ° and the angle of

depression of point B on the pole is 60 ° .

if O is the foot of the pole and OB = 20 m .

Find the distance between A and B .

leaving your answer in surd form .

Answered by sandy_suhendra last updated on 05/Jan/17

Commented by sandy_suhendra last updated on 05/Jan/17

∠ BPQ = 60 °

\tan 60 ° = \frac{BQ}{PQ}

\sqrt{3} = \frac{60}{PQ} \Rightarrow PQ = \frac{60}{\sqrt{3}} = 20 \sqrt{3} m

∠ APQ = 45 °

\tan 45 ° = \frac{AQ}{PQ}

1 = \frac{AQ}{20 \sqrt{3}} \Rightarrow AQ = 20 \sqrt{3} m

AB = BQ - AQ = (60 - 20 \sqrt{3}) m

Commented by tawakalitu last updated on 05/Jan/17

Wow . God bless you sir .