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To simplify the expression 25 cos 75 degrees, we first convert 75 degrees to radians:
75 degrees = 75 * π / 180 = 5π / 12 radians
Now, we can calculate the cosine of 5Ï€ / 12:
cos(5π / 12) ≈ 0.2588
Finally, we multiply this result by 25 to find the exact value of the force in the horizontal direction:
25 * 0.2588 ≈ 6.47 newtons
Therefore, the exact value of the force in the horizontal direction is approximately 6.47 newtons.