Final answer:
Using trigonometry and the law of sines, the length of the side opposite the 60° angle can be calculated when given the side length opposite the 75° angle and the angle measures. The specific formula for the side opposite the 60° angle is 14.0m * (sin(60°) / sin(75°)), which can be solved with a calculator.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on trigonometry. To find the length of the side opposite the 60° angle in a triangle with angles measuring 75°, 60° and a side opposite the 75° angle of 14.0m, we can use the law of sines. This law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles. In this case, we can set up our equation using the given 75° angle and its opposite side:
(side opposite 75°) / sin(75°) = (side opposite 60°) / sin(60°)
After isolating the side opposite the 60° angle and plugging in the known values, we can calculate its length:
side opposite 60° = 14.0m * (sin(60°) / sin(75°))
By computing this ratio using a calculator, we can find the length of the side opposite the 60° angle to the nearest tenth of a meter.