Answer:
D) 57.5°
Step-by-step explanation:
As the question is not complete. So, let's suppose it is a right angle triangle then, we can apply Pythagoras theorem to calculate the hypotenuse or the third side.
Pythagoras Theorem = [tex]c^{2}[/tex] = [tex]a^{2} + b^{2}[/tex]
a = 7 and b = 11
[tex]a^{2}[/tex] = 49
[tex]b^{2}[/tex] = 121
Plugging in the values, we will get:
[tex]c^{2}[/tex] = 49 + 121
[tex]c^{2}[/tex] = 170
c = [tex]\sqrt{170}[/tex]
To calculate the unknown angle B, we can use law of sine.
Law of sine = [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
So,
[tex]\frac{c}{sinC}[/tex] = [tex]\frac{b}{sinB}[/tex]
[tex]\frac{\sqrt{170} }{sin90}[/tex] = [tex]\frac{11}{sinB}[/tex]
Sin90 = 1
sinB = [tex]\frac{11}{\sqrt{170} }[/tex]
B = [tex]sin^{-1}[/tex] ([tex]\frac{11}{\sqrt{170} }[/tex])
B = 57.5°
