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Find the lengths of the missing sides in the triangle. Use the 45 degrees dash 45 degrees dash 90 degrees Triangle Theorem. Write your answers as integers, in radical form, or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.
A right triangle is shown with an angle that measures 45 degrees. The side opposite of the 45 degree angle is 7. The side opposite of the unlabeled angle is y. The side opposite of the right angle is x.
In a 45-45-90 degrees triangle, the sides are in a ratio of 1:1:√2.
We are given that the side opposite the 45-degree angle is 7, so the side opposite the right angle will also be 7.
The side opposite the unlabeled angle, y, will be in the same ratio as the other sides. Since the ratio is 1:1:√2, y will be equal to 7√2.
So, the lengths of the missing sides in the triangle are x = 7, y = 7√2.