Question - Solving for the Length of Legs in a 45-45-90 Triangle
Solution:
The image shows a right-angle triangle with a 45-degree angle. Since the angles in a triangle add up to 180 degrees and we already have a right angle (90 degrees) and one 45-degree angle, the other angle must also be 45 degrees. This makes the triangle a 45-45-90 triangle, which is a form of an isosceles right triangle.In a 45-45-90 triangle, the lengths of the legs (the two shorter sides) are equal, and the length of the hypotenuse (the longest side, opposite the right angle) is √2 times the length of a leg.The figure gives the hypotenuse as length 3. Therefore, to find the length of each leg (let's call it 'L'), we can use the proportion that L is to 3 (the hypotenuse) as 1 is to √2:L / 3 = 1 / √2Multiplying both sides by 3 to solve for L:L = 3 / √2To rationalize the denominator:L = (3 / √2) * (√2 / √2)L = (3√2) / 2So, the length of each leg of the triangle is (3√2) / 2 units.
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