To sketch this scenario, follow these steps:
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Draw a horizontal line to represent the level of point Y. Label this line as the ground level.
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Place point Y on the left side of the horizontal line. This is the point from which the angle of elevation is measured.
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From point Y, draw a line at an angle of 30 degrees above the horizontal line towards point X. This line represents the line of sight from Y to X.
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Mark the point X somewhere above the horizontal line along the line of sight from Y.
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Draw a vertical line from point X down to the horizontal line (ground level), and label this line as the height (h) from Y to X.
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Label the distance |XY| as 40 meters along the line of sight (the hypotenuse of the triangle formed by Y, X, and the point directly below X on the ground).
Now, to find the height of X above the level of Y, you can use trigonometry. Specifically, you can use the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
For this problem:
- \(\theta = 30^\circ\)
- The opposite side (height) is what we want to find, let's call it \(h\).
- The hypotenuse |XY| is 40 m.
Using the sine function:
\[ \sin(30^\circ) = \frac{h}{40} \]
Since \(\sin(30^\circ) = \frac{1}{2}\):
\[ \frac{1}{2} = \frac{h}{40} \]
Now, solving for \(h\):
\[ h = 40 \times \frac{1}{2} = 20 m \]
Thus, point X is 20 meters above the level of point Y.
You can visualize this setup by imagining a right triangle where:
- The angle at Y is 30 degrees,
- The hypotenuse (|XY|) is 40 m,
- The vertical height (h) from Y to X is 20 m.
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