Example Question - isosceles right triangle
Here are examples of questions we've helped users solve.
Solving for Leg Lengths in a 45-45-90 Triangle
The image shows a right triangle with one angle of 45 degrees and the hypotenuse having a length of 3 units. Given that the triangle is a right triangle with a 45-degree angle, we can infer that this is a 45-45-90 triangle, which is an isosceles right triangle. In such triangles, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg. Let's use the properties of a 45-45-90 triangle to find the lengths of the two legs. If \( a \) is the length of one leg, we have: \( a \cdot \sqrt{2} = 3 \) Now we solve for \( a \): \( a = \frac{3}{\sqrt{2}} \) To rationalize the denominator, we multiply the numerator and the denominator by \( \sqrt{2} \): \( a = \frac{3}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \) \( a = \frac{3 \cdot \sqrt{2}}{2} \) So both legs of the triangle are \( \frac{3 \cdot \sqrt{2}}{2} \) units long.
Solving the Length of the Hypotenuse in an Isosceles Right Triangle
The image shows a right triangle with one angle marked as 45 degrees, which means it is an isosceles right triangle (since the other non-right angle must also be 45 degrees). In such triangles, the legs are congruent. If the triangle is labeled with points G, J, and H, where GH is the hypotenuse, and the leg GJ is labeled as "4√2," then we can find the length of GH using the Pythagorean theorem. However, for an isosceles right triangle, we have a simpler relationship: In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. Given GJ = 4√2, the length of GH (the hypotenuse) is: GH = GJ * √2 GH = 4√2 * √2 GH = 4 * (√2 * √2) GH = 4 * 2 GH = 8 Therefore, the exact value of GH is 8, which corresponds to option C.
Solving for 'x' in an Isosceles Right Triangle
It appears from the image that we have a right triangle with one of the angles being 45 degrees, which makes it an isosceles right triangle. In such a triangle, the two legs are congruent, which means they have the same length. The question asks for the value of "x" in each right angle. Since "x" is marked on the vertical leg of the triangle, and given the 45-degree angle, we can infer that "x" will also be the length of the horizontal leg because of the properties of an isosceles right triangle (45-45-90 triangle). Therefore, the value of "x" will be the same for both the vertical and horizontal legs of the triangle. In this type of triangle, the legs are equal in length, so x = x for both the horizontal and vertical legs. No numeric value can be provided without additional information.
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