# In triangle ABC find: 1) side a if b = 11 cm, alpha = 45 degrees and gama = 120

In triangle ABC find: 1) side a if b = 11 cm, alpha = 45 degrees and gama = 120 degrees 2) side b, if c = 18 cm, alpha = 130 degrees and beta 27 degrees

1.

In the triangle ABC, we determine the value of the angle ABC.

Angle ABC = (180 – BAC – ACB) = (180 – 120 – 45) = 150.

By the sine theorem:

AC / SinABC = BC / SinBAC.

BC = AC * SinBAC / SinABC = 11 * Sin45 / Sin 15 = 11 * 0.71 / 0.26 = 30.04 cm.

Answer: BC length is 30.04 cm.

2.

In the triangle ABC, we determine the value of the angle ACB.

Angle ACB = (180 – BAC – ABC) = (180 – 130 – 27) = 230.

By the sine theorem:

AC / SinABC = AB / SinACB.

AC = AB * SinABC / SinACB = 18 * Sin27 / Sin 23 = 18 * 0.45 / 0.39 = 20.77 cm.

Answer: The length of the speaker is 20.77 cm.

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