Question #209906

from the top of an 80 ft building the angle of elevation of the top of the taller building is 49 degrees and the angle of depression of the base of this building is 62 determine the height of the taller building to the nearest foot


1
Expert's answer
2021-06-24T17:52:19-0400

let d be the distance between the buildingslet\ d\ be\ the\ distance\ between\ the\ buildings

let l be the difference between the height of the buildingslet\ l\ be\ the\ difference\ between\ the\ height\ of\ the\ buildings

tan(62)=80d=>d=80tan(62)\tan{\left(62^{\circ}\right)}=\frac{80}{d}=>d=\frac{80}{\tan{\left(62^{\circ}\right)}}

tan(49)=ld=ltan(62)80\tan{\left(49^{\circ}\right)}=\frac{l}{d}=\frac{l\tan{\left(62^{\circ}\right)}}{80}

l=tan(49)80tan(62)=48.9ftl=\tan{\left(49^{\circ}\right)}\ast\frac{80}{\tan{\left(62^{\circ}\right)}}=48.9ft

height of the taller building  49+80=129ftheight\ of\ the\ taller\ building\ \approx\ 49+80=129 ft


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