Answer:
- d
- b
- b
Explanation:
Trigonometry is a branch of mathematics that relates the measures of sides and angles in a triangle. The various trig functions of an angle are defined in terms of the sides of a right triangle containing that angle. Consequently, the Pythagorean theorem can be used to relate certain trig functions to each other, and to obtain formulas for the sum and difference of angles.
1. Solving triangles
The Pythagorean theorem relates side measures in right triangles. For relating side measures to each other or to angles in non-right triangles, one or both of the Law of Sines and the Law of Cosines must be used.
both b) and c)
2. Finding an angle
The Law of Sines relates side lengths and the sines of angles. Knowing three side lengths tells you nothing about the angles except the ratio of their sines.
The Law of Cosines relates three side lengths and one angle. Knowing the three side lengths, the angle measure can be found.
There is no Tangent Law.
3. Use of trigonometry
Trigonometry is a calculation tool, not a measuring tool. As such, it allows calculation of angles and sides (of a triangle) that cannot be physically measured.
Paintings benefit greatly from rules of proportion and perspective. In general, trigonometry is not directly involved. (Computer-generated art may implement these rules of perspective using trigonometry. Paintings, in general, make no direct use of trigonometry.)