NY Regents Geometry Law of Sines — practice questions

1. A right triangle has one angle of exactly 90 degrees. 2. Any triangle without such an angle is called an oblique triangle. 3. Obtuse and scalene describe only some oblique triangles, not all of them. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_

1. Two sides with the angle opposite one of them is the SSA arrangement. 2. The unknown side can swing to two different positions and still fit the data. 3. That is why SSA is called the ambiguous case, with zero, one or two triangles possible. 4. Two angles with any side fixes the third angle and scales the triangle uniquely. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_

1. The area is one half of the product of two sides and the sine of their included angle. 2. The sine of 30 degrees is 0.5. 3. So the area is 0.5 times 12 times 10 times 0.5. 4. That gives 30 square units. 5. Answering 60 square units forgets the leading one half in the formula. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_