From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Class 10th Mathematics Question Paper 2023 :From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Question :From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

The correct answer :Let’s draw a diagram to visualize the situation described:

In this diagram, the building is represented by point A, the top of the cable tower by point C, and the foot of the cable tower by point B. The height of the cable tower is represented by “h” meters.

We know that the angle of elevation from point A to point C is 60 degrees, so we can use the tangent function to find the distance between point A and point C:

tan(60) = h/AC

AC = h/√3

We also know that the angle of depression from point C to point B is 45 degrees, so we can use the tangent function again to find the distance between point A and point B:

tan(45) = AB/AC

1 = AB/(h/√3)

AB = h/√3

Now we can use the Pythagorean theorem to find the height of the cable tower:

AB^2 + BC^2 = AC^2

(h/√3)^2 + 7^2 = (h/√3)^2

49 = h^2/3

h^2 = 147

h ≈ 12.12 meters (rounded to two decimal places)

Therefore, the height of the cable tower is approximately 12.12 meters.