Question

what is ef?
ef =
submit
work it out

Explanation:

Step1: Apply the Hypotenuse - Leg (HL) Congruence Theorem

Since \( \angle EHG=\angle EFG = 90^{\circ}\), \( \angle HGE=\angle FGE = 70^{\circ}\), and \(EG\) is common to both right - triangles \( \triangle EHG\) and \( \triangle EFG\).
By the AAS (Angle - Angle - Side) congruence criterion (in right - triangles, we can also think of it in terms of the fact that if two angles and a non - included side are equal).
In \( \triangle EHG\) and \( \triangle EFG\):
\(\angle EHG=\angle EFG\), \(\angle HGE=\angle FGE\), \(EG = EG\) (common side)
So, \( \triangle EHG\cong\triangle EFG\)

Step2: Use the property of congruent triangles

If two triangles \( \triangle EHG\) and \( \triangle EFG\) are congruent, then their corresponding sides are equal.
We know that \(EH = 72\), and since \( \triangle EHG\cong\triangle EFG\), the corresponding side \(EF=EH\)

Answer:

\(72\)