Question 8 of 12intermediate🔧 ApplyNumerical4 marks

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Correct Answer

The height of the building is 50/3 m (or 16⅔ m).

Exercise: EXERCISE 9.1 | Q: 9 | (Page Page 10)
For More Understanding

Explanation

This problem involves two right triangles sharing the same base (distance between building and tower). Using tangent ratios from both observation points, we can establish two equations relating height and distance. Since the distance is the same, equating the expressions gives the unknown height.

Solution Steps

  1. Step 1: Let the height of the building be h m and the distance between the building and the tower be x m.

  2. Step 2: From the foot of the tower, angle of elevation to the top of the building is 30°. In right triangle formed: tan 30° = h/x, which gives 1/3\sqrt{3} = h/x, so x = h3\sqrt{3} ... (1)

  3. Step 3: From the foot of the building, angle of elevation to the top of the tower (50 m high) is 60°. In right triangle formed: tan 60° = 50/x, which gives 3\sqrt{3} = 50/x, so x = 50/3\sqrt{3} ... (2)

  4. Step 4: Equating equations (1) and (2): h3\sqrt{3} = 50/3\sqrt{3}, therefore h = 50/3 m.

  5. Step 5: Therefore, the height of the building is 50/3 m or 16⅔ m.

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