Question 4

The sine of the smallest angle in the triangle is 7/25.

In a triangle with side lengths 7, 24, and 25, the smallest angle is opposite the shortest side, which is 7. The sine of this angle can be calculated using the formula sin(θ) = opposite/hypotenuse, giving us sin(θ) = 7/25.

A) 7/25

This option is correct as it directly represents the sine of the smallest angle in the triangle. Since the smallest side length is 7 and the hypotenuse is 25, the sine function accurately reflects this relationship.

B) 24/25

This option is incorrect because it represents the sine of the angle opposite the side of length 24, which is larger than the angle opposite the side of length 7. Therefore, it does not correspond to the smallest angle in the triangle.

C) 25/24

This option is incorrect as it suggests a sine value greater than 1, which is not possible for any angle in a triangle. The sine function cannot exceed 1, and thus this choice is invalid.

D) 24/7

This option is incorrect because it suggests a sine value that would correspond to an angle opposite the side of length 24, which is larger than the angle opposite the side of length 7. Consequently, it does not represent the smallest angle in the triangle.

Conclusion

The correct answer, 7/25, accurately represents the sine of the smallest angle in the triangle, as it corresponds to the side opposite that angle. All other options fail to represent the sine of the smallest angle, either by being associated with larger angles or by exceeding the valid range of sine values.