Solve 13

Solve the missing dimensions for the following triangle: Triangle ABC: AngleA=43 degrees, b=7.0cm, c=6.0cm

Question 1. Angle B with units written as degrees
Question 2. Angle C with units written as degrees
Question 3. a, rounded to the nearest tenth of a cm with the unit.

Correct answer:

a =  4.8545 cm
B =  79.5497 °
C =  57.4503 °

Step-by-step explanation:

A=43  b=7.0 cm c=6.0 cm  a2 = b2+c2  2bc cos A  a=b2+c22 b c cosA=b2+c22 b c cos43° =72+622 7 6 cos43° =72+622 7 6 0.731354=4.855=4.8545 cm
sinB:sinA=b:a=7:4.85451.442=82653:57320 b0=sinA ab=sin43°  ab=sin43°  4.85457=0.681998 4.85457=0.98341  B=π180°arcsin(b0)=π180°arcsin0.9834=79.5497=79°3259"
sinC:sinA=c:a=6:4.85451.236=68968:55801 c0=sinA ac=sin43°  ac=sin43°  4.85456=0.681998 4.85456=0.84293  C=π180°arcsin(c0)=π180°arcsin0.842957.4503   Verifying Solution:   s=A+B+C=43+79.5497+57.4503=180 

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