an engineer is trying to find a width of a river there is two 42 degrees angles. the 19 meter is on the side. 19.7 meter is on the side then 15.4 meters on the left side
To find the width of the river, we can use trigonometry and the information provided.
Let's assume that the width of the river is represented by the letter 'x'.
From the given information, we have the following:
1. On the left side, there is a distance of 15.4 meters.
2. On the right side, there is a distance of 19 meters followed by a 42-degree angle.
3. On the right side, after the 42-degree angle, there is a distance of 19.7 meters.
Using the given information, we can create a diagram:
15.4 m 19 m 19.7 m
________ 42° ________________________
Now, we can use trigonometry to find the width of the river.
Since we have a triangle, we can use the law of sines.
The formula for the law of sines is:
sin(A)/a = sin(B)/b = sin(C)/c,
where A, B, and C are angles, and a, b, and c are the sides opposite to those angles.
In our case, we can use the angle C and the opposite sides 19.7 m and 19 m:
sin(42°)/19.7 = sin(180°-42°)/x,
simplifying the equation,
sin(42°)/19.7 = sin(138°)/x.
Now, we can solve for x:
x = (19.7 * sin(42°)) / sin(138°).
Evaluating this equation:
x ≈ 12.82 meters.
Therefore, the width of the river is approximately 12.82 meters.