How do you solve the triangle given C=15^circ15', a=6.25, b=2.15?

1 Answer
Douglas K.
Jan 29, 2017

Covert minutes to decimal degrees
Use The Law of Cosines to find the length of side c
Use The Law of Sines to find B
Use the sum of the interior angles equals 180^@ to find A

Explanation:

Use the factor 1^@/(60') to convert the minutes to decimal degrees:

(15')/1(1^@)/(60')= (15/60)^@ = 0.25^@

C = 15.25^@

Use The Law of Cosines to find the length of side c:

c=sqrt(a^2+b^2-2(a)(b)cos(C)

c=sqrt((6.25)^2+(2.15)^2-2(6.25)(2.15)cos(15.25^@)

c~~4.21

Use The Law of Sines to find B:

sin(B)/b = sin(C)/c

B = sin^-1(sin(C)b/c)

B = sin^-1(sin(15.25^@)2.15/4.21)

B~~ 7.72^@

To find A use the some if the interior angle equal 180^@:

A + B + C = 180^@

A + 7.72^@ + 15.25^@ = 180^@

A = 157.03^@

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