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Explanation & Answer
8.
Now for first triangle ,Cos (57 degree) = 21.8/x
x = 21.8 / Cos (57 degree)
x = 21.8 / 0.545
x = 40 cm
Now
Theta = 90 degree - 57 degree = 33 degree then
Cos (33 degree) = y / x
y = x * Cos (33 degree)
y = 40 * 0.838
y = 33.52 cm
9.
Now 92^2 = 54^2 + BC^2
BC^2 = 92^2 - 54^2
BC = √92^2 - 54^2
BC = √8464 - 2916
BC = √5548
BC = 74.5
Now for Angle C
Tan Angle C = 54 / 74.5
Angle C = Tan^-1(54 / 74.5)
Angle C = Tan^-1(0.7248)
Angle C = 35.9 degree
Now 180 degree = 96 degree + 35.9 degree + x
x = 180 degree - 96 degree - 35.9 degree
x = 48.1 degree
Now Cos (48.1 degree) = CD / CE
Cos (48.1 degree) = 61 / CE
CE = 61 / Cos (48.1 degree)
CE = 61 / 0.668
CE = 91.3
Hence CE = EC = 91.3
10.
Here 47 degree wire is higher, then
Now
Tan (47 degree) = x / 10
x = 10 * Tan (47 degree)
x = 10 * 1.072
x = 10.72 m
The higher wire is 10.72 m high.
Now
Tan (37 degree) = x / 10
x = 10 * Tan (37 degree)
x = 10 * 0.754
x = 7.54 m
The bottom wire is 7.54 m high.
Now 10.72 - 7.54 = 3.18 m
Hence The higher wire is 3.18 m high form bottom wire.
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