Sounds as tho' there were one or more illustrations with this problem. Could you possibly share the wealth?
If Triangle 1 has hyp 72 mm and one of the acute angles has measure alpha=52 deg., then the measure of the other acute angle must be (90-52), or 38 degrees.
We may now use the Law of Sines as a tool for calculating the lengths of the shorter sides alpha and beta:
a b c
----------- = ------------ = ----------------
sin alpha sin beta sin 90 deg.
Here,
c is the length of the hypo and is 72 mm;
Therefore
72 mm a
---------------- = ---------------- applies to the given data.
sin 90 deg sin 52 deg
(72 mm)(sin 52) = a(sin 90) = 1, so
(72 mm)(sin 52)
---------------------- = a = 56.74 degrees
1
and since the sum of the interior angles of the triangle must be 180, b = 180 - 56.74 deg., or beta = 33.26 deg.
