A radio must is supported by two wired on opposite sides. On the ground, the ends of the wires are 60 m apart. One wire makes a 62 degree angle with the ground and the other makes a 75 degree angle with the ground. To nearest tenth of a meter, how long are the wires, and how tall is the mast?
+128731 A radio must is supported by two wired on opposite sides. On the ground, the ends of the wires are 60 m apart. One wire makes a 62 degree angle with the ground and the other makes a 75 degree angle with the ground. To nearest tenth of a meter, how long are the wires, and how tall is the mast?
Let h be the height of the mast
Let the distance from where the wire that forms the 62 degree angle with the ground to the mast = x
So we have
tan ( 62) = h/x implies that xtan( 62 ) = h (1)
Next, let the distance from where the wire that forms the 75 degree angle with the ground to the mast = 60-x .......and we have
tan (75) = h / [60 -x] substitute for h and we have
tan (75) = [ x tan (62)] / [ 60-x] simplify......multiply both sides by 60-x
tan (75) [ 60 - x] = x tan (62)
60tan (75) - xtan (75) = x tan (62) add x tan (75) to both sides
60tan (75) = x tan(75) + xtan(62) factor out x
60tan(75) = x [ tan (75) + tan(62) ] divide both sides by [ tan (75) + tan(62) ]
60tan(75) / [ tan (75) + tan(62) ] = x = about 39.9 ft
So using (1), the height of the mast = x * tan(62) = 39.9 *tan(62) = about 75 ft
And the length of the wire that makes the 62 degree angle with the ground =
sin(62) = opp/ hyp .......so......
sin (62) = 75/length
length = 75/sin(62) = about 84.95 ft
And the length of the wire that makes the 75 degree angle with the ground =
sin(75) = opp/hyp ......so......
sin(75) = 75 / length
length = 75/sin(75) = about 77.6 ft
