You're standing on one side of a river that is 100 meters wide, and you want to determine the width of the river. You measure an angle of 60 degrees between your line of sight to the opposite bank and the direction perpendicular to the riverbank. How wide is the river?
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To solve this problem, we can apply basic trigonometry principles. Let's denote the width of the river as x meters.
We can consider a right-angled triangle where the width of the river is the opposite side, and the line of sight and direction perpendicular to the riverbank form the other two sides.
We have the following information:
- The opposite side (width of the river) is x meters.
- The angle between the line of sight and the direction perpendicular to the riverbank is 60 degrees.
In a right-angled triangle, the ratio of the opposite side to the hypotenuse is given by the sine of the angle:
sin(60°) = opposite side / hypotenuse
Simplifying this equation, we get:
sin(60°) = x / 100
By substituting the value of sin(60°) as √3 / 2, we can solve for x:
√3 / 2 = x / 100
Cross-multiplying, we find:
x = (√3 / 2) * 100 = (√3 * 100) / 2 = (100√3) / 2 = 50√3 ≈ 86.60 meters
Therefore, the width of the river is approximately 86.60 meters.
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