A telescope is placed on a tower 400 m away from a crossing. If the telescope has to be bent at an angle 15 degrees to the horizontal to see the crossing, what is the height of the tower.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A telescope is placed on a tower 400 m away from a crossing. To have a direct view of the crossing, the telescope has to be bent at an angle 15 degrees to the horizontal.

Let the height of the tower be H. The height H and the distance 400 m are related by the trigonometric identity tan 15 = H/400

=> H = 400*tan 15

=> H `~~` 107.17

The height of the tower is approximately 107.17 m

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