Question

a 149 ft tower is located on the side of a mountain that is inclined 21° to the horizontal. a guy wire is to be attached to the top of the tower and anchored at a point 49 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: Determine the angle of the triangle

The mountain is inclined at \(21^{\circ}\) to the horizontal. The tower is vertical. So the angle between the tower and the mountain - side is \(180^{\circ}- 90^{\circ}-21^{\circ}=111^{\circ}\)

Step2: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the angle \(C\) opposite to side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 149\), \(b=49\), and \(C = 111^{\circ}\), \(\cos(111^{\circ})\approx - 0.3584\)

Substitute the values into the formula:

$$
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Answer:

\(172.74\)