(Solved): 1. Consider the example of a building sign shown below (which was also an example discussed in clas ...

1. Consider the example of a building sign shown below (which was also an example discussed in class lectures). A sign weighing $500\mathrm{lb}$ is suspended from a cable, held at a distance of $20^{?}$ from the face of the building by a strut as shown. a) What is the total tension (lb) in the cable connecting the end of the strut to the building wall? Explain your answer (using words, geometry or algebra). Hint : you may assume that the force in the strut is purely horizontal - see the lecture notes for explanation about WHY this is true. b) How is the vertical component of the tension in the cable related to the angle of the cable (i.e. how will the vertical component of the tension in the cable change if we change the angle)? Explain your answer (using words, geometry or algebra). c) How is the total tension in the cable related to the angle of the cable? Explain your answer (using words, geometry or algebra). d) If we reduce the vertical distance between the cable attachment point and the hinge for the struct from $9\mathrm{ft}$ (example above) to $5\mathrm{ft}$, what will be the impact on the strut compression force. Can you figure out a way to make this calculation using ratios only, not using trig, per se? e) Considering the methods you used above, which would be most helpful in make quick estimates regarding design changes? Graphic methods? Trig? Ratios?