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
let d be the distance between the buildingslet\ 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\ 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(62∘)=d80=>d=tan(62∘)80
tan(49∘)=ld=ltan(62∘)80\tan{\left(49^{\circ}\right)}=\frac{l}{d}=\frac{l\tan{\left(62^{\circ}\right)}}{80}tan(49∘)=dl=80ltan(62∘)
l=tan(49∘)∗80tan(62∘)=48.9ftl=\tan{\left(49^{\circ}\right)}\ast\frac{80}{\tan{\left(62^{\circ}\right)}}=48.9ftl=tan(49∘)∗tan(62∘)80=48.9ft
height of the taller building ≈ 49+80=129ftheight\ of\ the\ taller\ building\ \approx\ 49+80=129 ftheight of the taller building ≈ 49+80=129ft
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