Answer
The tower is $\approx 203.5$ ft tall.
Work Step by Step
1. Find the angle opposite from the 270 ft length
Given that this is a right angled triangle, one if the angles is $90^{\circ}$ and the other is given by the question as $37^{\circ}$
Therefore the missing angle $ = 180 - (90 + 37) = 53^{\circ}$
2. Use the previous information in Step #1 and the sine law to solve for the height of the tower (Let $x =$ height of the tower)
$\frac{270}{sin53} = \frac{x}{sin37}$
$\frac{270sin37}{sin53} = x$
$\frac{270 \times 0.6018...}{0.7986...} = x$
$\frac{162.49...}/{0.7986...} = x$
$203.459... = x$
$x \approx 203.5$ ft
