One of the things we learned this week in Precalc 11 is how to use the cosine law to solve for angles or sidelengths of a triangle.
Cosine Law Formula
Sidelength | Angle |
---|---|
Laws
Since there are two laws, Sine and Cosine. To determine which law to use, look at one of the angles if there is one given, if the opposite side has a given sidelength then use the Sine Law, if the opposite side has an unknown sidelength then use the Cosine Law.
Solving for an angle
Solve for ∠B.
First we need to figure out what formula to use.
Next, we can fill in the the values.
Then we can do the calculations.
Solving for a sidelength
Solve for side c.
First figure out what formula to use.
Next, fill in the values.
Then do the calculations.
Examples
In △ABC, AB=7, ∠B=105°, and BC=10; determine side b to one decimal place.
first we need to draw what the triangle might look like, it doesn’t have to be accurate.
°
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