Trigging out.

March 19, 2007 10:06 PM

Trigonometry-related design problem inside.

Here's a diagram. A rectangle (ABCD) shares a corner with 28' segment a(1)a(2) at a(1). ABCD can be any size, but let's say for the sake of example that sides B/D are 24'.

If side C were to extend and form a line, that line must intersect a(2). What would be the angle formed between the segment and side B and what would be the distance from C to a(2) to ensure this?

posted by glibhamdreck to science & nature (3 comments total)

Hmm, this sounds a bit like a homework question, so it might be good to say why you're trying to figure this out. Rather than answer, I'll give you a hint:

The angle BC must be 90deg, so, you have a right triangle. Use the Pythagorean Theorem to calculate the length of Ca(2):
B^2 + Ca(2)^2 = a(1)(a2)^2.

To determine the angle, use any of the SOH-CAH-TOA trig relations (Sin theta = opposite/hypoteneuse, Cos theta = adjacent/hypoteneuse, Tan theta = opposite/adjacent).
posted by JMOZ at 10:21 PM on March 19, 2007

Not homework, just a garage added to house, actually. It's a lot simpler your way. I forgot it has to be a right triangle. Thanks.
posted by glibhamdreck at 12:18 AM on March 20, 2007

easy.
If you have a right triangle, then from your diagram:
28² = B² + ?²
If B is 24, then:
28² - 24² = ?²
1320 = ?²
36.33 = ?

tan(angle) = opposite side / adjacent side
tan(angle) = ? / B
tan(angle) = 36.33/24
angle = tan^-1(1.514)
angle = 56.56°
posted by plinth at 10:41 AM on March 20, 2007