Using relations in a right triangle, it is found that the length of AC is of 6.43 inches.
What are the relations in a right triangle?
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
In this problem, the length of side AC is b, which is opposite to the angle of 40º, while the hypotenuse is of 10 in, hence:
[tex]\sin{40^\circ} = \frac{b}{10}[/tex]
[tex]b = 10 \times \sin{40^\circ}[/tex]
Using a calculator:
[tex]b = 6.43[/tex]
More can be learned about relations in a right triangle at https://brainly.com/question/26396675
