Thread: More Missing Lengths

Well done!

Heres a harder one!

Part of a lifting device is shown in the diagram below. The longest member is called a tie bar and is angled at 70° to the horizontal. The other long member is called the strut and is angled at 80° to the horizontal. The length of the base is 1.4 m. (Find all the missing lengths & angles)

Well, we know the angle between the longer members is 10 degrees, because of the angles of the members to the horizontal.
We also know the larger acute angle in the triangle is 70 degrees; this too comes from the given information.
This the obstuse angle is 180 - 70 - 10 = 100 degrees.
By the law of sines, 1.4/(sin 10) = (strut)/(sin 70) = (tie bar)/(sin 100)
Thus, the tie bar is about 7.940 m long, and the strut is about 7.576 m long.