In △ABC shown below, 𝑆𝑖𝑛𝐶=45 and the length of AB is 10 inches. What is the length, in inches, of 𝐴𝐶― ?
Question
In △ABC shown below,
𝑆𝑖𝑛𝐶=45 and the length of AB is 10 inches. What is the length, in inches, of 𝐴𝐶― ?
Solution
The question seems to be missing the diagram of triangle ABC. However, based on the given information, we can assume that angle C is opposite side AC.
In a right triangle, the sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse.
So, if SinC = 45, then we have:
SinC = AC/AB
Rearranging the equation to solve for AC gives:
AC = AB * SinC
Substituting the given values:
AC = 10 * Sin45
The Sin45 is approximately 0.7071 (in most cases you can use this approximation).
So,
AC = 10 * 0.7071 = 7.071 inches
Therefore, the length of AC is approximately 7.071 inches.
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