Step-by-step explanation:
The interior angles of any triangle must add up to 180° in measure. Right angles have measure 90°, so the missing angles in both triangles here have measure 45°.
In a 45°-45°-90° triangle, the legs and hypotenuse occur in a ratio of 1 : √2. This means
(1) x = 48 √2
(2) 88 = √2 x → x = 88 / √2 = 44 √2
You could also set up trigonometric equations to solve for x in each case:
(1) cos(45°) = 48 / x → x = 48 / cos(45°) = 48 / (1 / √2) = 48 √2
(2) cos(45°) = x / 88 → x = 88 cos(45°) = 88 (1 / √2) = 44 √2
