Question

The angle of depression of the top and bottom of a building 50 m high building from the top of the tower are 45 and 60 respectively find the height of the tower and horizontal distance between the tower and building.(use root 3= 1.73)

Answer 1

let AB=50m be ht of building CD be the ht. of tower draw AE perpendicular on CD. join AD andBD to form two triangles ADE and DBC in which <DAE=45 and <DBC=60 in rt. <d. triangle DEA DE/AE=tan45 : DE/AE=1 Or DE=AE .. in rt. <d . DCB ; DC/BC=tan60 Or DC/AE= 1.732 or 50 +DE/ AE=1.73 :; Or 50+AE/AE =1.73 ;; or 50 +AE= 1.73 AE ;;; 50 =1.73AE-AE :; AE(1.73- 1)= 50:;; or. 0.73 AE= 50 ;; AE =50/0.73 :: also CD=CE+DE Or CD=50+AE which will be the height of tower