Question

CAN SOMEONE PLS HELP?? IM AB TO FAIL GEOMETRY AND NEED HELP W LAW OF SINES. PLEASE

Answer 1

Part a) In ΔABC, c = 5.4, a = 3.3, and m∠A=20° . What are the possible approximate lengths of b? Use the law of sines to find the answer.

we know that

$\frac{sin\ A}{a} =\frac{sin\ B}{b} =\frac{sin\ C}{c}$

Step $1$

Find the value of angle C

$\frac{sin\ A}{a} =\frac{sin\ C}{c}$

$\frac{sin\ 20}{3.3} =\frac{sin\ C}{5.4}\\ \\ sin\ C=\frac{5.4*sin\ 20}{3.3} \\ \\ sin\ C=0.5597\\ \\ C=arcsin(0.5597)\\ \\ C=34\ degrees$

Step $2$

Find the value of angle B

we know that

$A+B+C=180\\ B=180-(A+C)\\ B=180-(20+34)\\ B=126\ degrees$

Step $3$

Find the value of side b

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

$\frac{sin\ 20}{3.3} =\frac{sin\ 126}{b}\\ \\ b=\frac{3.3*sin\ 126}{sin\ 20} \\ \\ b=7.8\ units$

Step $4$

Find the alternative angle C

$C=180-34\\ C=146\ degrees$

Find the alternative angle B

$A+B+C=180\\ B=180-(A+C)\\ B=180-(20+146)\\ B=14\ degrees$

Find the alternative value of side b

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

$\frac{sin\ 20}{3.3} =\frac{sin\ 14}{b}\\ \\ b=\frac{3.3*sin\ 14}{sin\ 20} \\ \\ b=2.3\ units$

therefore

the answer Part a) is the option

$C:\ 2.3\ units\ and\ 7.8\ units$

Part b) What is the approximate value of k? Use the law of sines to find the answer

Step $1$

Find the value of angle J

we know that

$J+K+L=180\\ J=180-(K+L)\\ J=180-(120+40)\\ J=20\ degrees$

Step $2$

Find the value of side k

$\frac{sin\ K}{k} =\frac{sin\ J}{j}$

$\frac{sin\ 120}{k} =\frac{sin\ 20}{2}\\ \\ k=\frac{2*sin\ 120}{sin\ 20} \\ \\ k=5.1\ units$

therefore

the answer Part b)

$k=5.1\ units$

Answer 2

The laws of sines is already indicated in the provided images.

1. sin20/3.3 = sinC/5.4
Thus, angle C is 34.03 degrees. To find angle B: 180 - 20 - 34.03 = 126 degrees. Using the law of sines,

sin20/3.3 = sin(126)/b
b = 7.8 units

From this answer, we can already tell that the answer is letter C: 3 units and 7.8 units.

2.  Angle J = 180 - 120 - 40 = 20 degrees. Then,

sin(20)/2 = sin(120)/k
k = 5.1 units