Question

Eiffel Tower : The Eiffel Tower is a landmark and an early example of wrought-iron construction on a gigantic scale. The lower section consists of four immense arched legs set on masonry piers. The legs curve inward until they unite in a single tapered tower. Platforms, each with an observation deck, are at three levels; on the first is also a restaurant. The tower, constructed of about 7000 tons of iron, has stairs and elevators. A meteorological station, a radio communications station, and a television transmission antenna, as well as a suite of rooms that were used by Eiffel are located near the top of the tower. (i) For a person standing \( 324 m \) from the center of the base of the Eiffel Tower, the angle of elevation to the top of the tower is \( 45^{\circ} \). How tall is the Eiffel Tower? (ii) A car is moving at uniform speed towards the Eiffel tower. It takes 15 minutes for the angle of depression from the top of tower to the car to change from \( 30^{\circ} \) to \( 60^{\circ} \). After how much time after this, the car will reach the base of the tower?

Answer 1

(i)

Let AB be the height of the Eiffel Tower;

Let 'C' be the point where the person is standing from the centre of the base of the Eiffel Tower;

Now, in triangle ABC,

Tan45° = AB/BC;

1 = h/324;

h = 324 m;

•The height of the Eiffel Tower is 324m;

(ii)

We know that :

Distance = Speed × Time;

Let the Speed of the car be 'v';

Let DC be the distance travelled by the car in 15 minutes;

Let the distance travelled by the car after 15 minutes be 'xv';

First, in triangle ABC,

Tan60° = AB/BC;

√3 = 324/xv;

xv = 324/√3; -(i)

Now, in triangle ABD,

Tan30° = AB/BD;

1/√3 = 324/xv+15v;

xv+15v = 324√3;

xv+15v = 3xv; [3 × xv = 3 × 324/√3 = 324√3]

15v = 2xv;

x = 15/2 = 7.5;

•The car will reach the tower in another 7.5 minutes.

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