Me with this asap quickly brainliest

Problem One

Remark

This uses the Cosine Law. Two sides and an included angle leaves you with no choice. The good news is that there is never any ambiguity.

Step One

Find the supplement to the 105 degree angle. The supplement will put you inside the triangle which you need to have happen for the cos law.

180 - 105 = 75

Step Two

Set up the Cos Law, You will be solving for b

b^2 = a^2 + c^2 - 2*a*c*Cos(B)

Givens

a =200

B = 75 from step one.

c = 180

Solve

b^2 = 200^2 + 180^2 - 2*180*200*cos(75)

b^2 = 40000 + 32400 - 72000 * cos(75)

b^2 = 72400 - 72000 * 25882

b^2 = 72400 - 18634.97

b^2 =53756.03

b = sqrt(53765.03)

b = 231.9

Problem Two

This is the Sine Law

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

Find C

C = 180 - B - A

C = 180 -37.81 - 113.17

C = 29.02 The sin law will give an ambiguity if you use 12 and 113.17. Better to use an acute angle if you can with the sine law.

Solve

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

b / sin(37.81) = 6.33/sin(29.02)

b / 0.6130 = 6.33 / 0.4851

b / 0.6130 = 13.048

b = 13.048 * 0.6130

b = 7.9987 which rounds to 8.

Answer D <<<<

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)