To determine the width of the river, which is represented by DG, we will use trigonometric ratios. The following are the steps to solve the problem:
1. Recognize that EG is a bisector: This means that it cuts angle DEF into two equal angles. Since angle DEF is given as 60°, each of the two angles, DEG and EGF, will be 30°.
2. Identify the right triangle: The triangle DEG is a right triangle with angle DEG as 30° and angle DGE as 90° (since FG is perpendicular to DE).
3. Apply trigonometric ratios: In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our triangle DEG, DG is the opposite side to angle DEG, and FG is the hypotenuse.
Since angle DEG is 30°, we know from trigonometry that:
sin(30°) = 1/2
This tells us that the length of the opposite side (DG) is half of the length of the hypotenuse (FG) in any right triangle with a 30° angle.
4. Calculate DG: FG is given as 20 meters. Therefore, to find DG, we take half of FG:
DG = 1/2 * FG = 1/2 * 20 m = 10 m
So, the width of the river (DG) is 10 meters.
