Question

what is eh?
(diagram: points g, f, e with right angles at g and e, angle at f is 64° (twice), hg = 81, eh = )

Explanation:

Step1: Identify the triangles

We have two right triangles, \( \triangle FGH \) and \( \triangle FEH \). The angles at \( F \) are both \( 64^\circ \), and \( \angle FGH \) and \( \angle FEH \) are right angles (\( 90^\circ \)). Also, \( FH \) is a common hypotenuse.

Step2: Determine congruence or equal sides

Since the angles at \( F \) are equal, and both triangles are right - angled, by the Angle - Angle - Side (AAS) congruence criterion, \( \triangle FGH\cong\triangle FEH \). In congruent triangles, corresponding sides are equal. We know that \( FG = FE \) (not directly used here), and the side \( HG = 81 \). Since \( \triangle FGH\cong\triangle FEH \), the corresponding side \( EH=HG \).

Answer:

\( 81 \)