Strength of Materials
Problem Assignment - Trigonometry
1. A 40 ft long ladder leaning against a wall makes an angle of 60° with the ground. Determine the vertical height to which the ladder will reach. (answers at bottom of problem set.)
2. In the roof truss shown, the bottom
chord members AD and DC have lengths of 18ft. and 36ft
respectively. The height BD is 14 ft. Determine the lengths of the top
chords AB and BC and find the angles at A and C.
3. One side of a triangular lot is 150 ft. and the angle opposite this side is 55°. Another angle is 63°. Sketch the shape of the lot and determine how much fencing is needed to enclose it.
4. An Egyptian pyramid has a square base and symmetrical sloping faces. The inclination of a sloping face is 42° 08'. At a distance of 500 ft. from the base, on level ground the angle of inclination to the apex is 25° 15'. Find the vertical height(h), the slant height of the pyramid, and the width of the pyramid at its base.
#5. Triangle ABC shown is a triangular tract of land. The one acre tract DEFG is to be subdivided. AE is 500ft and DC is 300 ft. Determine the lengths of DG and CB. [This is a harder problem and may be skipped.]
Some Answers 1. H =34.64'; 2. AB=22.8', BC=38.6', A = 37.9o, C = 21.25o; 3. L=474.8'; 4. h=411.3', slant = 554.6', width=744.2' 5. ED=68.4', DG=677.4', CB=1035'
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