Question #153926

A 100 foot wire is extended from the ground to the top of a 60 foot pole, whish is perpendicular to the level ground. Find to the nearest degree, the measure of the angle that the wire makes with the ground.


1
Expert's answer
2021-01-07T13:47:43-0500


Here in the image, AB is the 60ft tall pole and AC is the 100ft tall wire.

As \angle ABC is 90o90^o , we use trigonometry:


sinθ=ABAC=60ft100ft=60100=35sin\theta=\frac{AB}{AC}=\frac{60ft}{100ft}=\frac{60}{100}=\frac{3}{5}

Therefore we have,

sinθ=35θ=sin1(35)θ0.643536.8698osin\theta=\frac{3}{5}\\ \Rightarrow \theta=sin^{-1}(\frac{3}{5})\\ \Rightarrow \theta\approx0.6435\approx36.8698^o




Therefore the angle that the wire makes with the ground is 36.8698o.36.8698^o.


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