Question

Does anyone have the answers for this?!

Answer 1

We don't need the answers.  Let's do the problems.

In triangle ABC with sides a,b,c labeled in the usual way, the Law of Sines is

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

Side a is opposite vertex A, etc.

1. A=46, B=29, a=x, b=5

a/sin A = b/sin B

a = b(sin A)/sin B

x = (5) sin 46 / sin 29 = 7.41878636786

Answer: x=7.4

2.  We don't have to spell it all out with a, b and c.

x/sin 65 = 22/sin 53

x = 22 (sin 65)/sin 53 = 24.96604654309146

Answer: x=25.0

3. x/sin 15 = 12/sin 128

x = 12 sin 15/sin 128 = 3.941352991713482

Answer: 3.9

4. x = 18 sin 73 / sin 59 =  20.081827192002002 = 20.1

5. Trickier, we need the missing angle 180-19-26=135

x = 32 sin 19 / sin 135 = 14.73353278 = 14.7

6. 180-78-75=27

x = 28 sin 27 / sin 75 = 13.16015541 = 13.2

7. 180-51-70=59

x = 9 sin 59 / sin 70 = 8.20960549830328 = 8.2

8. 180-52-33=95

x/ sin 33 = 16/sin 95

x = 16 sin 33 / sin 95 = 8.747511482 = 8.7