Law of Sines

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 = 46⁰ and side c = 35 cm
What is the length of angle 3 and sides A and B

sin 460 35	=	sin 1000 B

B sin 46⁰ = 35 sin 100⁰

B = (35 sin 100⁰)/sin 46⁰

B ≈ 47.917 cm

angle 3 = 180⁰ - 46⁰ - 100⁰ = 34⁰

sin 460 35	=	sin 340 A

A sin 46⁰ = 35 sin 34⁰

A = (35 sin 34⁰)/sin 46⁰

A ≈ 27.208 cm


The Law of Sines is:

sin∠ 2 C	=	sin∠ 1 B	=	sin∠ 3 A

Notice the relationship of the angles to the sides.

Try this problem:

∠1 = 110⁰  ∠3 = 50⁰  side A = 40.3 cm

Find ∠3 and sides B and C

answer

next law of cosine

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