Problem

Triangles Unit Test If a right triangle has a leg with length 12 and the hypotenuse is 16 , how long is the other leg? Round to the nearest tenth, if necessary. (1 point)

Solution

Step 1 :Given that the length of one leg (a) is 12 units and the length of the hypotenuse (c) is 16 units in a right triangle.

Step 2 :We can use the Pythagorean theorem to find the length of the other leg (b). The Pythagorean theorem is expressed as \(a^2 + b^2 = c^2\).

Step 3 :Rearranging the equation to solve for b, we get \(b^2 = c^2 - a^2\).

Step 4 :Substituting the given values into the equation, we get \(b^2 = 16^2 - 12^2\).

Step 5 :Calculating the squares and subtracting, we get \(b^2 = 256 - 144\).

Step 6 :So, \(b^2 = 112\).

Step 7 :Taking the square root of both sides to solve for b, we get \(b = \sqrt{112}\).

Step 8 :Rounding to the nearest tenth, we get \(b \approx 10.6\).

Step 9 :So, the length of the other leg is approximately \(\boxed{10.6}\) units.

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Source: https://solvelyapp.com/problems/DNZq0y7XZz/

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