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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.
By the 45-45-90 Triangle Theorem, in a 45-45-90 triangle, the two legs are congruent. Therefore, the side opposite the unlabeled angle is also 7.
Using the theorem again, we know that in a 45-45-90 triangle, the length of the hypotenuse is equal to the length of a leg times √2.
Thus, the length of the hypotenuse x is 7√2.
Answer:
The length of the side opposite the unlabeled angle is 7.
The length of the hypotenuse is 7√2.