# chs

posted by peter

Two wires support an electricity pole. if the wires make angles of 58°and 67° with the ground and |AB|=21m, calculate the lengths of the wires

1. Steve

Draw a diagram. If the pole has height h, then

h = 21/(cot58°-cot67°) = 104.8

The two wires have length

104.8 csc67° = 113.9
104.8 csc58° = 123.6

2. Dave

sorry steve you failed
All angles of a triangle add up to 180
degrees, so you have 2 angles you can
Find the third angle by 180-58-67=55

Now use the law of sines...(capital
is the angle and lower case the
side across from said angle

you have the 3 angles now and 1 side
use law of sines
a/sinA=b/sinB=c/sinC
(law of cos is for if you know sides
but not angles)
(law of tan if you know 3 of the 4
unknowns c^2=a^2+b^2-2abcos(C) )

well the top angle(C) is 55
which means AB would be across from
it being 21
so
a/sin58=b/sin67=21/sin55

so because c=21/sin55=
a=21/sin(55 deg)*sin(58 deg)
b=21/sin(55 deg)*sin(67 deg)

so
a = 21.7407868825
b = 23.5983076125

now just test this using tan

(remember bedmas order of operations)
2*21.7407868825*23.5983076125*cos(55 deg)
=588.541936444
=2*
21.7407868825^2+23.5983076125^2
=1029.541936444
1029.541936444-588.541936444
=441
441 on the nose!

and i have been out of school for 20 years

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