Question

a 149 ft tower is located on the side of a mountain that is inclined 23° to the horizontal. a guy wire is to be attached to the top of the tower and anchored at a point 65 ft downhill from the base of the tower. find the shortest length of wire needed.
note: the picture is not drawn to scale.
length of guy-wire = ft
enter your answer as a number; your answer should be accurate to 2 decimal places.
question help: video

Explanation:

Step1: Find the included angle

The mountain is inclined at \(23^{\circ}\) to the horizontal. The tower is vertical. So the included angle \(\theta=90^{\circ}+ 23^{\circ}=113^{\circ}\)

Step2: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the included angle \(\gamma\) opposite side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos\gamma\). Here, \(a = 149\), \(b=65\), \(\gamma = 113^{\circ}\)

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Answer:

\(184.39\)