Question 3

A = 1/2(4.1)(3.2) sin (25°)

The area of triangle ABC can be accurately calculated using the formula A = 1/2ab sin(C), where 'a' and 'b' are the lengths of two sides and 'C' is the included angle. In this case, using sides of lengths 4.1 and 3.2 with an included angle of 25° correctly gives the area.

A) A = 1/2(4.1)(3.2) sin (25°)

This option correctly applies the formula for the area of a triangle using the lengths of the two sides, 4.1 and 3.2, and the sine of the included angle, 25°. Therefore, it accurately calculates the area of triangle ABC.

B) A = 1/2(1.7)(3.2) sin (25°)

This option incorrectly uses the length of one side as 1.7 instead of 4.1. While it follows the correct formula structure, using the wrong side length leads to an inaccurate calculation of the area.

C) A = 1/2(4.1)(1.7) sin (25°)

Here, the option substitutes the side length of 3.2 with 1.7, which is incorrect. Although it uses the correct formula, the area calculation is flawed due to the incorrect side length being used.

D) A = 1/2(4.1)(3.2)(1.7) sin (25°)

This option misapplies the area formula by introducing an unnecessary multiplication of a third side length (1.7) along with the sine of the angle. The correct formula only requires two sides and the sine of the included angle, rendering this option incorrect.

Conclusion

Option A is definitively the correct choice as it correctly uses the lengths of the sides 4.1 and 3.2 along with the sine of the angle 25° to compute the area of triangle ABC. All other options fail due to incorrect side lengths or misapplication of the area formula, resulting in inaccurate area calculations.