a telephone pole is 10m high. a wire is tethered from the topof of the pole to a
ID: 3096194 • Letter: A
Question
a telephone pole is 10m high. a wire is tethered from the topof of the pole to a peg on the ground. let x be the angle ofinclination the wire makes with the ground. a)determine an equation that relates thelength of the wire, l, to the angle of inclination of thewire. b)determine the equation that relates thedistance, d, of the peg from the base of the pole, to theangle of inclinatoin, x. c)what angle will be made when 15m of wireis used? at what distance will the peg me planted? a telephone pole is 10m high. a wire is tethered from the topof of the pole to a peg on the ground. let x be the angle ofinclination the wire makes with the ground. a)determine an equation that relates thelength of the wire, l, to the angle of inclination of thewire. b)determine the equation that relates thedistance, d, of the peg from the base of the pole, to theangle of inclinatoin, x. c)what angle will be made when 15m of wireis used? at what distance will the peg me planted? c)what angle will be made when 15m of wireis used? at what distance will the peg me planted?Explanation / Answer
C | | l 10 | |__x B d A BC = 10m AC = l m AB = d m a) The equation is: sin (x) = 10m / l or l sin (x) = 10m b) The equation is: tan (x) = 10m / d or d tan (x) = 10m c) with l = 15m, we can now use the Pythagoreantheorem: AB2 + BC2 = AC2 d2 + 102 = 152 d2 + 100 = 225 d2 = 225 -100 d = 11.18m We can calculate x by knowing that sin (x) = 10/15 = 2/3. x = sin-1 of 2/3 x = 41.81 degrees
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