(10) MTH1.3: The Sine Law
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10 Terms
Acute Triangle
A triangle with three angles less than 90°.
Sine Law/Law of Sines
A formula that relates a triangle’s sides to the sines of their opposite angles: a/SinA = b/sinB = c/sinC. It is used to find an unknown side or angle on any triangle when you know at least one side–angle pair.
In Sine Law:
When each side of a triangle is divided by the sine of its opposite angle, you will get the same common value because all the ratios are equal. The proportions can also be flipped.
The sine formula suggested when solving for an unknown side:
a/sinA = b/sinB = c/sinC.
The sine formula suggested when solving for an unknown angle:
sinA/a = sinB/b = sinC/c.
The Condition of Sine Law
You must know either: (1) two sides and one angle across from a known side (SSA), or (2) two angles and any side (ASA).
Mathematical Proof
A logical, step-by-step argument that shows a statement is always true, not just based on examples or trial-and-error.
Perpendicular
A line, plane, or surface that intersects with another at a right angle (90°).
How to Find an Angle Using the Sine Law
(1) Label all known sides and angles, and match each side with its opposite angle, (2) Write the Sine Law formula for angles and substitute the values, (3) Cross-multiply, (4) Isolate for sinθ by dividing, and (5) Isolate for the angle by multiplying the inverse sin.
How to Find a Side Using the Sine Law
(1) Label all known sides and angles, and match each side with its opposite angle, (2) Write the Sine Law formula for angles and substitute the values, (3) Cross-multiply, and (4) Isolate for the side by dividing.