1) The angle of elevation to the bottom of a transmission tower on a hill from an observer standing 1.8 km away from the base of the hill is 5 degrees. The angle of elevation to the top of the tower from the tower is 6.8 degrees. If the distance from the observer to the base is 1.8 km, find the height of the tower to the nearest metre.

Answer 1

Tan5 = Y1/X = Y1/1.8
Y1 = 1.8*Tan5 = 0.157 km = Ht. of hill.

Tan6.8 = (Y1+Y2)/X = (Y1+Y2)/1.8
Y1+Y2 = 1.8*Tan6.8 = 0.215 km
Y2 = 0.215-Y1 = 0.215-0.157 = 0.058 km. = 58 m. = Ht. of tower.