Question

1. compute the length of piece ab of the roof truss in figure 35–74.

figure 35–74
a b is the top base of a 2.2 meters high trapezoid with a 10.3 meters bottom base and 35.3 and 28.5 degrees side angles.

Explanation:

Step1: Find horizontal segments

For the left triangle (with angle \(35.3^\circ\)) and height \(h = 2.20\) m, the horizontal segment \(x_1\) is \(x_1=\frac{h}{\tan(35.3^\circ)}\). For the right triangle (with angle \(28.5^\circ\)), the horizontal segment \(x_2=\frac{h}{\tan(28.5^\circ)}\).

Step2: Calculate \(x_1\) and \(x_2\)

\(\tan(35.3^\circ)\approx0.710\), so \(x_1=\frac{2.20}{0.710}\approx3.099\) m. \(\tan(28.5^\circ)\approx0.540\), so \(x_2=\frac{2.20}{0.540}\approx4.074\) m.

Step3: Find length of \(AB\)

The bottom base is \(10.30\) m. \(AB = 10.30-(x_1 + x_2)\). \(x_1 + x_2\approx3.099 + 4.074 = 7.173\) m. So \(AB\approx10.30 - 7.173 = 3.127\) m (approx 3.13 m, depending on precision).

Answer:

\(\approx 3.13\) meters (or more precise value based on calculator steps)