Let’s find the angles of the triclinic crystal! A triclinic crystal has all sides and angles different. The triclinic crystal we’re dealing with is a prism. All of its sides are parallelograms. With faces with areas 30cm2, 35cm2, and 42cm2, it could be orthorhombic, with all right angles. That would give it sides 5cm, 6cm, and 7cm, but we know that those aren’t the side lengths. It could also have 1 right angle, and then it could have sides 3cm, 11cm, and 14cm. 3*10 = 33, and 3*14 = 42. And 11*14 = 154. 90 degree angles give the biggest area, so 2 bigger areas are fine. If you didn’t know about triclinic crystals, you’d probably guess that. It’s the obvious solution. But for no angles to be 90, all the products have to be higher than necessary. The 33 must go to 30. The 42 can’t go to 42, the 154 must. And so the 42 goes to 35. 33>30, 42>35, and 154>42. No problem. The portion of the area is the sin of the angle. Simple trig. So our answers are arcsin(30/33), arcsin(35/42), and arcsin(42/154), which gives us 65.38°, 56.44°, and 15.83°.