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!

Related questions
See all questions in The Law of Sines
Impact of this question
1452 views around the world
You can reuse this answer
Creative Commons License