Respuesta :
Answer: 2nd and 3rd statement
Step-by-step explanation:
From the diagram, the 1st statement is wrong, the 2nd statement is correct
To know which of the rest of the statement is correct we have to find the value of MN
So we use the cosine rule to find the angle inside the triangle at point L
c2 = a2+b2-2abcosC
For our triangle
c= 12.8
b= 5.9+5.9=11.8
a= 3.7+3.7=7.4
C = ?
(12.8)2 = (7.4)2 + (11.8)2 - 2x11.8x7.4cosC
163.84 = 54.76+739.24 - 174.64cosC
163.84 = 194 - 174.64cosC
163.84-194 = -174.64cosC
-30.16 = -174.64cosC
-30.16/-174.64 =cosC
cosC = 0.1727
cos-1(0.1727) = 80.06
C = 80.06 degrees
So we use this value to find length MN with also cosine rule from the triangle NML
c2 = a2+b2-2abcosC
c = ?
a = 5.9
b = 3.7
C = 80.06
c2 = (5.9)2 + (3.7)2 - 2x5.9x3.7cosC
c2 = 34.81 + 13.69 - 43.66x0.1727
c2 = 48.5 - 7.54
c2 = 40.96
c = root(40.96)
c = 6.4
Which is half of KJ
So therefore, the third statement is correct
