Here we want to use what we know about trigonometry to find the side of a triangle.
We will see that the correct option is B.
First, we know that the sum of all internal angles of a triangle is 180°.
Then the missing angle of the triangle, let's call it C, is given by:
A + B + C = 180°
75° + 45° + C = 180°
C = 180° - 45° - 75° = 60°.
Now we can use the sine rule, it says that the sine of an angle over the length of the opposite side of the triangle is a constant, then we have:
[tex]\frac{sin(A)}{BC} = \frac{sin(B)}{AC} = \frac{sin(C)}{AB}[/tex]
Here the length of the string is AC.
And we know that:
B = 45°
C = 60°
AB = 240
Then we can use the second and third parts of the above equality to get:
[tex]\frac{sin(45 \°)}{AC} = \frac{sin(60 \°)}{240}[/tex]
Now we can solve this for AC:
[tex]AC = \frac{sin(45 \°)}{sin(60 \°)}*240 = \frac{2 }{\sqrt{3*2}}*240[/tex]
Now we can multiply and divide by √6
[tex]AC = \frac{\sqrt{6} }{\sqrt{6} } *\frac{2}{\sqrt{6} }*240 = \frac{\sqrt{6} }{3}*240 = \sqrt{6} *80[/tex]
Then we can see that the correct option is B.
If you want to learn more, you can read:
https://brainly.com/question/19501516