Question - Solving for Legs of a 45-45-90 Triangle
Solution:
The image shows a right triangle with one angle marked as 45 degrees and the hypotenuse labeled as 3 units long.This is an isosceles right angle triangle since one angle is 45 degrees, meaning that the other non-right angle is also 45 degrees because the two acute angles in a right triangle always add up to 90 degrees. In an isosceles right triangle, the legs (the two sides that are not the hypotenuse) are congruent, meaning they have the same length.To solve for the lengths of the legs, we can use the Pythagorean theorem or a knowledge of the properties of a 45-45-90 triangle. In a 45-45-90 triangle, the hypotenuse is √2 times longer than either of the legs.Let's call the length of each leg 'x'. According to the special properties of a 45-45-90 triangle: hypotenuse = leg * √2Since the hypotenuse is 3 units, we can formulate the following equation:3 = x * √2To find 'x,' divide both sides of the equation by √2:x = 3 / √2To rationalize the denominator, multiply the numerator and denominator by √2:x = (3 * √2) / (√2 * √2)x = (3 * √2) / 2Therefore, the length of each leg of the triangle is 3√2/2 units.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com