Question

Find sin(lbac - 60��) for A = 13, B = 12, C = 5.

1) 6/5
2) 13/6
3) 13/5
4) 26/5
5) 5/2613
6) 6/13v3
7) 6.3

Answer 1

The value of sin(∠ BAC - 60°) for a triangle with sides A = 13, B = 12, and C = 5 is
`\( (6)/(13√(3)) \)` (Option 6).

Step-by-step explanation:

The expression sin(∠ BAC - 60°) involves finding the sine of the angle difference between angle BAC and 60 degrees. In a triangle, the Law of Cosines can be used to find the cosine of an angle:

cos(∠ BAC) = B² + C² - A²/2BC

For the given triangle with sides A = 13, B = 12, and C = 5:

cos(∠ BAC) = 12² + 5² - 13²/2 . 12 . 5} = 144 + 25 - 169/120 = -1/4

Now, using the trigonometric identity sin θ =
`√(1 - \cos^2(\theta)) \)`, we can find sin(∠ BAC):

sin(∠ BAC) =
`\sqrt{1 - \left(-(1)/(4)\right)^2} = (√(15))/(4) \]`

Finally, sin(∠ BAC - 60°)can be calculated as
`\( (√(15))/(4√(3)) \)`, which simplifies to
`\( (6)/(13√(3)) \)`. Therefore, the correct answer is Option 6,
`\( (6)/(13√(3)) \)`.