Answer:
GE = 62√3
Step-by-step explanation:
The interior angles of a triangle always sum to 180°. Therefore, the missing angle in right triangle ABC is 45°, and the missing angle in right triangle AGE is 30°.
Right triangle ABC is a special 45-45-90 triangle. In such a triangle, the sides are in the ratio 1 : 1 : √2, which means the legs are of equal length. Since leg BC measures 58 units, leg AB also measures 58 units.
Segment BG is the sum of segments BA and AG. Given that BG = 120 units and BA = 58 units:
BA + AG = BB
58 + AG = 120
AG = 120 - 58
AG = 62
Right triangle AGE is a special 30-60-90 triangle. In these triangles, the sides are in the ratio 1 : √3 : 2, which means the longer leg is √3 times the length of the shorter leg. Since AG = 62 units, we have:
[tex]\LARGE\boxed{\boxed{\sf GE = 62\sqrt{3}}}[/tex]
