To find the exact values of b and c in the given triangle, we can use the trigonometric ratios.
Let's label the angle opposite side b as angle B, and the angle opposite side c as angle C.
We know that the sum of angles in a triangle is 180 degrees. Therefore, angle A = 180 - 45 - 90 = 45 degrees.
Now, we can use the tangent ratio:
tan B = opposite/adjacent = b/16
tan 45 degrees = 1
Therefore, b = 16 * 1 = 16
Next, we can use the sine ratio:
sin C = opposite/hypotenuse = c/45
sin 90 degrees = 1
Therefore, c = 45 * 1 = 45
So, the exact values of b and c are b = 16 and c = 45.
