Question

Solve triangle ABC given that A = 56°, B = 57°, and b = 9.00. Round the length of the sides to the nearest hundredth

Answer 1

Answer:

Part 1) $C=67^o$

Part 2) $a=8.90\ units$

Part 3) $c=9.88\ units$

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the interior angles of any triangle must be equal to 180 degrees

so

$A+B+C=180^o$

substitute the given values

$56^o+57^o+C=180^o$

$C=180^o-113^o=67^o$

step 2

Find the length side a

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{a}{sin(56^o)}=\frac{9.00}{sin(57^o)}$

solve for a

$a=\frac{9.00}{sin(57^o)}sin(56^o)$

$a=8.90\ units$

step 3

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(67^o)}=\frac{9.00}{sin(57^o)}$

solve for c

$c=\frac{9.00}{sin(57^o)}sin(67^o)$

$c=9.88\ units$