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Geometry/Applications of Trigonometry

Question
How do you solve a triangle ABC given that angle A=60°, b=8cm and c=12cm?

The law of cosines says that a² = b² + c² - 2 * b * c * [cos A].
Since the b is known, c is known, and cos 60° is 1/2, that gives
a² = 8² + 12² - 2*8*12/2 = 64 + 144 - 96 = 112.
This means the value of a is the square root of 112.

Using the law of sines, the rest of the angels can be found.
The law of sines says that for any triangle, (sin A)/ a = (sin B)/ b = (sin C)/c.

All we need to know we already have in that c = 12, sin C = root(3)/2,
so using a we can find angel A and using b we can find angle B.

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