Question

what is gj?
55
46°
46°
gj =
submit

Explanation:

Step1: Identify the type of triangles

We have two right triangles, \( \triangle HIJ \) and \( \triangle HGJ \), with a common angle of \( 46^\circ \) and right angles at \( I \) and \( G \) respectively. Also, \( IJ = 55 \) (given as the length of the vertical side in \( \triangle HIJ \)).

Step2: Use the property of congruent triangles or equal - length sides

Since the two triangles have two angles equal (right angle and \( 46^\circ \) angle) and the sides opposite the right angles (the other pair of non - hypotenuse sides) should be equal if the triangles are congruent in terms of the side we are interested in. Alternatively, we can use the fact that in the figure, the side \( GJ \) and \( IJ \) are equal because the triangles are set up such that the corresponding sides (perpendicular to the parallel lines \( I \) - \( H \) and \( G \) - related lines) with the same angle of \( 46^\circ \) will be equal. So, \( GJ=IJ \). Given \( IJ = 55 \), we can conclude that \( GJ = 55 \).

Answer:

\( 55 \)