Answer:
₩⁰
Step-by-step explanation:
first of all : that is NOT how the penalty area looks like and is used in soccer. for example, a penalty is always kicked from a central point 11 meters away from C.
anyway, to get the angle CAE, we need to get CAB, then based on this we calculate further to EAB.
and then CAE = EAB - CAB
we have right-angled triangles. and we use Pythagoras and the law of sine :
c² = a² + b²
a/sinA = b/sinB = c/sinC
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the other 2 sides (typically called legs).
A, B, C are the corresponding opposite angles.
remember, sin(90°) = 1.
CA² = (a + 12)² + b² = (58 + 12)² + 52² = 70² + 52² =
= 4900 + 2704 = 7604
CA = sqrt(7604) = 87.20091743... ft
CA/sin(90°) = (a+12)/sin(CAB) = 70/sin(CAB)
sin(CAB) = 70×sin(90°)/CA = 70/87.20091743... =
= 0.802743848...
CAB = 53.39292519...°
EA² = (a + 12 + 12)² + 52² = 82² + 52² = 6724 + 2704 =
= 9428
EA = sqrt(9428) = 97.09788875... ft
EA/sin(90°) = (a+12+12)/sin(EAB) = 82/sin(EAB)
sin(EAB) = 82×sin(90°)/EA = 82/97.09788875... =
= 0.844508578...
EAB = 57.61932229...°
CAE = EAB - CAB = 57.61932229... - 53.39292519... =
= 4.226397106...° ≈ 4.2°
