How do you solve a triangle given angle A = 18.27°, angle C = 134.13°, side A = 8.3?

1 Answer
Shantelle
May 27, 2018

color(red)(B = 27.6)

color(red)(c ~~ 19.003) (rounded to nearest thousandth's place)

color(red)(b ~~ 12.266) (rounded to nearest thousandth's place)

Explanation:

First, we know that the angles of a triangle add up to 180^@. We have two angles (A and C), so we can find B by doing:
180^@ - 18.27^@ - 134.13^@ = 27.6

Therefore, angle color(red)(B = 27.6).

Now, use the Law of Sines to solve for side c:

c/sinC = a/sinA

c/sin134.13^@ = 8.3/sin18.27^@

c = (8.3sin134.13)/sin18.27^@

Therefore,
side color(red)(c ~~ 19.003)

Since we have two sides and an angle (or more), we can use the Law of Cosines to solve for the last side, b.

The Law of Cosines is b = sqrt(a^2 + c^2 - 2(a)(c)(cosB)

Let's plug in our values into the formula:
b = sqrt((8.3)^2 + (19.003)^2 - 2(8.3)(19.003)(cos27.6^@))

b = sqrt(68.89 + 361.114 - 279.553)

b = sqrt(430.004 - 279.553)

b = sqrt(150.451)

Therefore,
color(red)(b ~~ 12.266) (rounded to nearest thousandth's place)

Hope this helps!

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