Answer
Two angles in one triangle are congruent to two angles in the other triangle, so the triangles are similar according to the AA Similarity Postulate.
$x = 180$ ft.
Work Step by Step
These two triangles are similar because two angles are congruent, so they are similar according to the AA Similarity Postulate.
One angle in each triangle is a right angle, and right angles are congruent.
Two angles are vertical angles; therefore, these angles are congruent because vertical angles are congruent.
If two triangles are similar, then their sides are proportional. Let's find the scale factor for a pair of sides first:
$\frac{90}{135}$
Divide both the numerator and denominator by their greatest common factor, $45$:
$\frac{2}{3}$
This gives:
$\frac{120}{x} = \frac{2}{3}$
Cross multiply to get rid of fractions:
$2x = 360$
Divide each side by $2$ to solve for $x$:
$x = 180$ ft.
