# Law of Sines

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Many triangles are oblique meaning that they are not right triangles.

Yet we still want to find the length of their sides and angles. To measure the length of

these angles and sides we use the law of sines and law of cosines.

If angle 1 = 100 ^{0} angle 2 = 46^{0} and side c = 35 cm

What is the length of angle 3 and sides A and B

B sin 46^{0} = 35 sin 100^{0}

B = (35 sin 100^{0})/sin 46^{0}

B ≈ 47.917 cm

angle 3 = 180^{0} - 46^{0} - 100^{0} = 34^{0}

A sin 46^{0} = 35 sin 34^{0}

A = (35 sin 34^{0})/sin 46^{0}

A ≈ 27.208 cm

The Law of Sines is:

Notice the relationship of the angles to the sides.

Try this problem:

∠1 = 110^{0} ∠3 = 50^{0} side A = 40.3 cm

Find ∠3 and sides B and C

answer

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