A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height 7 m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30° and that of the top of the flag-staff is 45°. Find the height of the tower.

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Solution

Let BC be the tower of height h m. AB be the flag staff of height 7 m on tower and D be the point on the plane making an angle of elevation of the top of the flag staff is 45° and angle of elevation of the bottom of the flag staff is 30°.

Let CD = x, AB = 7 and and.

We to find height of the tower

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle

Again in a triangle

Hence the height of tower is m.

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flag-staff are respectively $60^{\circ} a n d 45^{\circ}$ . Find the height of the flag-staff and that of the tower.

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