A 145-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (Round your answer to the nearest foot.)

By apply the law of cosine, the shortest length of wire needed is 180 feet.How to determine the shortest length of wire needed?In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.In Trigonometry, law of cosine (cos) is given by this mathematical expression:C² = A² + D² - 2(A)(D)cosDNote: Angle D = 90° + 32° = 122°Substituting the given parameters into the formula, we have;C² = 55² + 145² - 2(55)(145)cos122°C² = 3,025 + 21,025 - 2(7,975)(-0.5299)C² = 24,050 - (-8,451.905)C² = 24,050 + 8,451.905C² = 32,501.905C = √32,501.905C = 180.28 ≈ 180 feet.Read more on law of cosine here: https://brainly.com/question/13756263#SPJ1