QQuestion
From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between ships A and B to the nearest metre. Use mathematical tables.
✓Answer
Let CD be the tower, with C as its foot and D as its top.
CD = 100 m.
The angles of elevation from A and B equal the corresponding angles of depression.
Therefore, ∠A = 45° and ∠B = 38°.
In △ACD:
⇒ tan 45° = \frac{CD}{AC}
⇒ 1 = \frac{100}{AC}
⇒ AC = 100 m
In △BCD:
⇒ tan 38° = \frac{CD}{BC}
⇒ 0.7813 = \frac{100}{BC}
⇒ BC = \frac{100}{0.7813}
⇒ BC ≈ 127.99 m
Since the ships are on opposite sides:
⇒ AB = AC + BC
⇒ AB = 100 + 127.99
⇒ AB = 227.99 m
Therefore, the distance between the ships, to the nearest metre, is 228 m.
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