Answer:
x = 13, y = 18.38
Step-by-step explanation:
The problem can be solved in two ways. Either using geometry, or trigonometry.
Solution #1: Geometry
The described triangle is right, and one of the other given angles in this triangle is valued at 45 degrees. Therefore, we can infer that the other angle is also 45 degrees (180 - 90 - 45 = 45 degrees), and so the triangle is equilateral. Therefore, x = 13.
To find the hypotenuse, we can use the pythagorean theorem.
[tex]13^2 + 13^2 = y^2\\\to 169 \times 2 = y^2\\\to 338 = y^2\\\to y = 18.38[/tex]
Solution #2: Trigonometry
We can use the tan() function to find x. This function is described as the relationship between an angle to the ratio between the side opposite of said angle and the side adjacent to said angle, that isn't the hypotenuse.
[tex]\tan(45) = \frac x{13}\\\to 1 = \frac x{13}\\\to x = 13[/tex]
To find y, we can once again either use the pythagorean theorem, or use the sine/cosine functions. For this example, I'll use the sine function, which is described as the relationship between an angle and the ratio between the side opposite of said angle and the hypotenuse. (Cosine is the same, but with the side adjacent to the angle instead of the one opposite to it.)
[tex]\sin(45) = \frac {13}y\\\to \frac{\sqrt2}2 = \frac{13}y\\\to y = 13\sqrt{2} \approx 18.38[/tex]
