In Belleville, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 6.6 kilometres and the distance between the courthouse and the city pool is 8.2 kilometres, how far is the library from the community pool? If necessary, round to the nearest tenth.

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Identify Relationship: Identify the relationship between the library, courthouse, and community pool to determine the shape formed by their locations. The library, courthouse, and community pool form a right triangle with the library at the right angle.Determine Triangle Sides: Determine the sides of the right triangle. The distance between the library and the courthouse is one leg of the triangle, and the distance between the courthouse and the community pool is the other leg. The distance between the library and the community pool is the hypotenuse.Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the distance between the library and the community pool. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a^2 + b^2 = c^2.Plug in Known Values: Plug in the known values into the Pythagorean Theorem. Let a = 6.6 km (library to courthouse), b = 8.2 km (courthouse to pool), and c = the distance from the library to the pool. 6.6^2 + 8.2^2 = c^2Calculate Squares: Calculate the squares of the known sides. 6.6^2 = 43.56 8.2^2 = 67.24Add Squares: Add the squares of the known sides to find the square of the hypotenuse. 43.56 + 67.24 = 110.8Calculate Hypotenuse Length: Calculate the square root of the sum to find the length of the hypotenuse. c^2 = 110.8 c = sqrt(110.8) c ≈ 10.5 km (rounded to the nearest tenth)

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