Math Problem Statement
A restaurant owner attaches a sign to the side of his building as shown in the image. A beam is bolted to the building to support the cable, and the cable is anchored to the end of the beam and tensioned such that it bears the full weight of the sign. The beam is exactly horizontal with respect to the earth, the upper portion of cable makes a 38.2o angle with the beam, and the mass of the sign is 10.8 kg.
Determine the magnitude of the force exerted on the beam. Report your answer in Newtons.
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Forces and Tensions
Vector Resolution
Formulas
Weight (W) = m * g
Tension vertical component (Ty) = W
Total Tension (T) = Ty / sin(θ)
Horizontal Force (Tx) = T * cos(θ)
Theorems
Newton's Second Law
Trigonometric Ratios
Suitable Grade Level
Grades 10-12
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