Question

A 116 ft tower is located on the side of a mountain that is inclined 33° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 67 ft downhill from the base of the tower. Find the shortest length of wire needed. 116f 67A 330 NOTE: The picture is NOT drawn to scale. Round all answers to 3 decimal places. Length of guy-wire = ft

Answer 1

Given, A.C= 67ft BC = 116ft L BAD = 33* (by property of В T 116ft corresponding angle) A now, SMDCAD: D 33 simo = =) sim 33°= 67 =) 67* sim 33° =p 36.491 3t = now, coso = b h COS 33° 6 =) 67xcos 33 = AD 15 56:19). = AD SOI = BCTCD - BD = 116+ 36.491 => BD = 152.991

now, In A ABD: using pythagoream sule: b2 = 52 + b? -) (AB)2 = (BD)2 + (DA)? =) (AB)2 = (152.491)2 + ( 56.191)? =) (AB)2 = 23253.50 5081 + 3157.428481 =) AB 26410.933562 => AB = 162.514 ft. Hence, length of guy wire is 162.514 feet.