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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.
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.
(2 points)
Since the triangle is a right triangle and one angle measures 45 degrees, it must be a 45-45-90 triangle. In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is sqrt(2) times the length of a leg.
Given that the side opposite the 45 degree angle is 7, we can determine that both legs are 7 units long. Therefore, the length of the side opposite the right angle (hypotenuse) is 7*sqrt(2) ≈ 9.9.
So, the missing side lengths are:
- x (opposite the right angle) ≈ 9.9 units
- y (opposite the unlabeled angle) = 7 units