HEIGHT AND DISTANCE
FROM A POINT A ON THE GROUND, THE ANGLE OF ELEVATION OF THE TOP OF A 20 m TALL BUILDING IS 45. A FLAG IS HOSTED AT THE TOP OF THE BUILDING AND THE ANGLE OF ELEVATION OF THE TOP OF THE FLAGSTAFF FROM A IS 60. FIND THE LENGTH OF THE FLAGSTAFF AND THE DISTANCE OF THE BUILDING FROM THE POINT A. LET "BC" BE THE BUILDING AND "BD" BE A FLAG GIVEN, BC=20 m ANGLE(BAC)=45 ANGLE(DAC)= 60 LET BD= x m IN TRIANGLE(BAC), tan45 = BC/AC = 20/AC AC = 20 m NOW IN TRIANGLE(DCA), DC = DB + BC = x + 20 tan 60 = DC/AC sqrt(3) = (x + 20)/20 x + 20 = 20*sqrt(3) = 20 * 1.732 = 34.64 x = 34.64 - 20 = 14.64 m HENCE, THE LENGTH OF THE FLAGSTAFF IS 14.64 M AND DISTANCE OF POINT A FROM THE BUILDING IS 20 m. TWO POLES ARE PLACED AT P AND Q ON EITHER SIDE OF A ROAD SUCH THAT THE LINE JOINING P AND Q IS PERPENDICULAR TO THE LENGTH OF THE ROAD. A PERSON MOVES x METRE AWAY FROM P ...