The angle of elevation from the top of a small building to the top of a nearby taller building is 46°40', while the angle of depression to the bottom is 14°10'. If the smaller building is 28 meters high, find the height of the taller building.

- Mar 4th 2010, 03:27 AMsomanyquestions[SOLVED] height of a building using angles of elevation & depression
The angle of elevation from the top of a small building to the top of a nearby taller building is 46°40', while the angle of depression to the bottom is 14°10'. If the smaller building is 28 meters high, find the height of the taller building.

- Mar 4th 2010, 04:05 AMSudharaka
Dear somanyquestions,

Please refer to the attached drawing.

$\displaystyle y=\frac{28}{tan14^{o}10'}$

$\displaystyle y=110.93$

$\displaystyle tan46^{o}40'=\frac{x}{y}=\frac{x}{110.93}$

Therefore, x=117.57

Height of the tall building=x+28=145.57m

Hope this will help you.