Answer:
A
Step-by-step explanation:
Ah...Trigonometry is fun!
The law of sines states:

The transitive property (switching the orders of the equations) applies here. Therfore, we can say that

We then plug in our given values to find C


Solving, we get 0.8557316387.
We're not done yet!We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).
arcsin0.8557316387 (arcsin is the same as inverse sin)
=
58.8 (approximate)
So the measure of angle C is 58.8. You could check this by reinserting it into the equation

.
:)
Answer: the boy won 10 games
Step-by-step explanation:
Let's call B as the number of games won by the boy, and F as the number of games won by the father.
We know that, there is a total of 26 games:
B + F = 26.
We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:
B*8 + F*(-5) = 0.
Then we have a system of equations:
B + F = 26
8*B - 5*F = 0.
The first step is isolating one of the variables. Let's start isolating F in the first equation:
B + F = 26
F = 26 - B.
Now we can replace this in the second equation:
8*B - 5*F = 0
8*B - 5*(26 - B) = 0
8*B + 5*B - 5*26 = 0
13*B = 5*26
B = 5*26/13 = 5*2 = 10
So the boy won 10 games (then the father won the other 16 games)