How do you solve a triangle given <A=84.2°, <B=20.7°, B=17.2?

1 Answer
Apr 24, 2016

Answer:

The following diagram represents your problem

Explanation:

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Step 1:

Since we know an angle opposite a known side, we can use the Sine Rule to solve for side a.

#sinA/a = sinB/b = sinC/c#

#sin84.2/a = sin20.7/17.2 = sinC/c#

#a = (17.2 xx sin84.2)/sin20.7#

#a = 48.4#

Step 2:

We could have done this at first, but let's find angle C. We know that the sum of the three angles in a triangle always equals 180. Therefore, we can set up the following equation:

#C + 20.7 + 84.2 = 180#

#C = 180 - 20.7 - 84.2#

#C = 75.1˚#

Step 3:

We must now substitute the value of angle C to find side C.

#SinB/b = sinC/c#

#sin20.7/17.2 = sin75.1/c#

#(17.2 xx sin75.1)/sin20.7 = c#

#47.0 = c#

Summary:

Your triangle has the following dimensions:

#/_A = 84.2˚#
#/_B = 20.7˚#
#/_C = 75.1˚#

#a = 48.4# units
#b = 17.2# units
#c = 47.0# units

Hopefully this helps!