A tower subtends an angle α on the same level as the foot of the tower and at a second point h metres above the first, the depression of the foot of the tower is β. Show that the height of the tower is h tan α cot β.
Heights & Distances
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Question

A tower subtends an angle α on the same level as the foot of the tower and at a second point h metres above the first, the depression of the foot of the tower is β. Show that the height of the tower is h tan α cot β.

Heights & Distances

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KnowledgeBoat · Accepted Answer

Let AB be the tower of height H and C be a point on the same horizontal level as B. Let D be a point vertically above C such that CD = h. Let BC = x. From right angled ΔABC, we get From right angled ΔDBC, we get From (1) and (2), we have Hence, the height of the tower is h tan α cot β.

Mathematics

A tower subtends an angle α on the same level as the foot of the tower and at a second point h metres above the first, the depression of the foot of the tower is β. Show that the height of the tower is h tan α cot β.

Heights & Distances

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