### Problem On heights And Distances

Check us out at http://www.tutorvista.com//videos If the distance of a person from a tower is 100 m and the angle subtended by the top of the tower with the ground is 30o, what is the height of the tower in meters? Steps: •Draw a simple diagram to represent the problem. Label it carefully and clearly mark out the quantities that are given and those which have to be calculated. Denote the unknown dimension by say h if you are calculating height or by x if you are calculating distance. •Identify which trigonometric function represents a ratio of the side about which information is given and the side whose dimensions we have to find out. Set up a trigonometric equation. •Substitute the value of the trigonometric function and solve the equation for the unknown variable. Solution: •AB = distance of the man from the tower = 100 m •BC = height of the tower = h (to be calculated) •The trigonometric function that uses AB and BC is tan A , where A = 30o. So tan 30o = BC / AB = h / 100 Therefore height of the tower h = 100 tan 30o = (100) 1/√3 = 57.74 m.

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