Problema Solution

At a point 30 meters from the base of a tower, the distance to the top of the tower is 2 meters more than twice the height of the tower. Find the height.

Answer provided by our tutors

let


a = 30 m the distance from the base of the tower to the point

c = the distance from the point to the top of the tower, c>0

b = the height of the tower, b>0


the distance to the top of the tower is 2 meters more than twice the height of the tower


c = 2 + 2b


we will use the Pythagorean Theorem since a, b and c are sides of a right triangle (a and b are legs and c is hypotenuse)


b^2 = c^2 - a^2


plug c = 2 + 2b and a = 30 into the equation


b^2 = (2 +2b)^2 - 30^2


by solving we find


b = 16 m


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the height of the tower is 16 meters.