2017 · Q54
A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From these observations, the breadth of the river will be (Given that tan α° = 2 and tan β° = 0.5)
Elementary MathematicsTrigonometry
- A60 m
- B70 m
- C80 m
- D90 m
Explanation
Let the river breadth be w and the tower's foot be u east of X's meridian. From X: tan α = u/w = 2, so u = 2w. From Y (200 m east): tan β = (200−u)/w = 0.5, so 200−u = 0.5w. Substituting u = 2w: 200 = 2.5w, giving w = 80 m. Hence option (C) 80 m.