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After some searching I found:

  • Triangulation
  • Using theta and "b" to find out the height of a building.

Thanks in advance.

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    $\begingroup$ The second one you mention is more properly known as "shadow reckoning". :) $\endgroup$ – J. M. isn't a mathematician Oct 20 '10 at 15:58
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    $\begingroup$ I feel like this question would be better asked to architects than mathematicians. (I certainly don't know anything about actual architecture.) $\endgroup$ – Qiaochu Yuan Oct 20 '10 at 16:12
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    $\begingroup$ Architects use CAD software. You can be sure trigonometry is used all over the pace when writing such software! $\endgroup$ – Mariano Suárez-Álvarez Oct 20 '10 at 16:13
  • $\begingroup$ @Qiaochu sadly though, there's no Architecture stackexchange site $\endgroup$ – aviraldg Oct 21 '10 at 9:42
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Too many to name. Anything that involves the study of the measure of triangles is trigonometry. The Egyptians used Pythagorean triplets to produce right angles using the "rope stretching method." (a circular rope with 12 knots. stretch so that you have 3, 4, 5)

So, it has played a role as long as architecture has been architecture.

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