By using the law of sine, the measure of ∠C is 39°
Law of sine:
Law of sine refers the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
Given,
Here we have the triangle.
Now, we have to find the angle ∠C.
While we looking into the given diagram,
We have the length of,
AB = 6
AC = 9
∠B = 105°
So, based on the law of sine it can be written as,
=> sin 105° / 9 = sin x°/6
Apply the value of sin 105° = 0.97, then we get,
=> 0.97/9 = sin x° / 6
Cross multiply them, then we get,
=> 5.82/9 = sin x°
=> 0.64 = sin x°
=> x = sin⁻¹ (0.64)
=> x = 39°
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