How do you find the measure of angle B for the triangle with the following dimensions. A = 71° , a = 9.3, b = 8.5?

1 Answer
Meave60
Aug 18, 2015

#"B=59.8"^"o"#
Use the law of sines: #"a"/("sinA")="b"/"sinB"="c"/"sinC"#.

Explanation:

Law of sines: #"a"/("sinA")="b"/"sinB"="c"/"sinC"#.

#"A=71"^"o"#
#"a"=9.3#
#"b"=8.5#
#"B=?"#

Since there are no values for side c and angle C, we can ignore this ratio. Since we have the sides a and b, but don't have angle B, we can invert the ratios for the law of sines.

#("sinA")/"a"=("sinB")/"b"# =

#("sin71"^"o")/8.5=("sinB")/9.3#

Divide #"sinA"# by side #"a"#.

#0.101669=("sinB")/8.5#

Multiply both sides by #8.5#.

#0.101669xx8.5="sinB"#

#0.8641865="sinB"#

Switch sides.

#"sinB"=0.8641865#

Determine angle #"B"# by taking the inverse sin of #0.85#.

#"B=sin"^(-1)(0.8641865)#

#"B=59.8"^"o"#

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