Question

from the fop of building of 20 meter high. the angle of depresion of the top and button of pole are observed to be 45 ond 60 respectively .find the height of the pole and distance between the pole.​

Answer 1

let AB be the height of tower & CD be the height of pole. let BC be the distance between pole and tower

angle BAD =angleD=60`(alternate interior angles)

tan 60`=60/BD

root 3 =60/BD

BD =60/root 3

construction - draw a line ED parralel to BD at top of pole. draw line AO parralel to BD & extend CD to point O.

now angle OAD= angle ADE (alternate interior angles)

tan 45`=AE/ED

ED=BD =60/root 3 (as EDCB is a parallelogram )

DC=AB-AE

DC=60- 60/root 3

DC=(60×root 3 - 60)/root 3 [after rationalizing]

DC=60-root 3 or 20×root 3 (root 3 - 1)

Answer 2

Step-by-step explanation:

$Let the height of the pole be h and the distance between the pole and tower be x.</p><p></p><p>It can be observed that,</p><p></p><p>tan60∘=x50</p><p></p><p>3=x50</p><p></p><p>x=350</p><p></p><p>And,</p><p></p><p>tan45∘=x50−h</p><p></p><p>1=x50−h</p><p></p><p>50−h=x</p><p></p><p>50−h=350</p><p></p><p>h=50−350</p><p></p><p>h=350(3−1)</p><p></p><p>h=21.1m</p><p></p><p>Therefore, the height of the pole is 21.1m.</p><p></p><p>$