Answer:
a = 4.64
c = 6.57
B = 75
Step-by-step explanation:
Law of sines in a triangle:
a, b and c are the sides.
A, B and C are the angles.
They are related in the following way:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Applying the law to the triangle in this question:
[tex]\frac{a}{\sin40}^{^{}}=\frac{7}{\sin B}=\frac{c}{\sin65}[/tex]
The internal angles of a triangle add up to 180º
65 + B + 40 = 180
105 + B = 180
B = 75
So
[tex]\frac{a}{\sin40}^{^{}}=\frac{7}{\sin 75}=\frac{c}{\sin65}[/tex]
The sines are:
sin 40º = 0.64
sin 75º = 0.966
sin 65º = 0.906
Finding a:
[tex]\frac{a}{\sin 40}=\frac{7}{\sin 75}[/tex][tex]\frac{a}{0.64}=\frac{7}{0.966}[/tex]
Applying cross multiplication:
0.966a = 7*0.64
a = (7*0.64)/0.966
a = 4.64
Finding c:
[tex]\frac{7}{\sin 75}=\frac{c}{\sin 65}[/tex][tex]\frac{7}{0.966}=\frac{c}{0.906}[/tex]
0.966c = 7*0.906
c = 7*0.906/0.966
c = 6.565
