You are given two sides of a triangle, x$=5\mathrm{.}7$ and y$=8\mathrm{.}3.$ The angle between them is $48$ degrees.

Write a C program to find the length of the third side and the area of the triangle.

$2$ It's the final moments of a crucial soccer match. The score is tied, and the team's star player,

Alex, has the ball at midfield, $50$ yards away from the goal. The goal is guarded by a $6-$foot$-$tall

goalkeeper. Alex decides to take a shot on goal, kicking the ball at a $40$ angle to the ground.

a$.$ Write a C program to determine how fast Alex must kick the ball so that it reaches the goal $50$

yards away, neglecting air resistance.

b$.$ Perform a brief experiment using your program to determine if there was a better angle at

which Alex could have kicked the ball to ensure it clears the goalkeeper's $6-$foot reach at the goal

line.

$3$ Write a script that validates the relationship between sin$(),$ cos$(),$ and tan$()$ by evaluating

these functions at suitably chosen values of $.$

$4$ You have a circle with a radius of $3$ centered at x$=2,$ y$=4.$ You want to calculate the

intersection of certain lines with that circle.

Write a C program to find the x and y coordinates of both points of intersection. You should test

this code at least with these lines:

$$ y $=0\mathrm{.}5$ x $+1$

$$ y $=$x $+8$

$$ y $=2$x $6\mathrm{.}5$