Engineering Board Exam Reviewer · Solutions to Oblique Triangles · hard
ECE Board April 1998: Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32° W of N and from B the bearing of C is 26° N of E. Approximate the shortest distance of tower C to the highway.
- 364 m
- 374 m
- 384 m
- 394 m
Answer
B. 374 m
Solution
Let h be the perpendicular distance from tower C to the highway, with foot of perpendicular at horizontal distance x from A. The bearing from A gives h=x 58° (90°-32°) and the bearing from B gives h=(1000-x) 64° (90°-26°). Solving simultaneously gives h 374 m.
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