To address a problem involving a ladder leaning against a wall at a 68-degree angle, we typically need to apply some basic trigonometry principles. The most upvoted solutions often focus on deriving the relationship between the length of the ladder (hypotenuse), the height it reaches on the wall (opposite side), and the distance from the wall to the base of the ladder (adjacent side).
Here’s how you can set up the problem:
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Identify the triangle: By leaning the ladder against the wall, you form a right triangle where:
- The length of the ladder is the hypotenuse \( L \).
- The height the ladder reaches on the wall is the opposite side \( h \).
- The distance from the wall to the base of the ladder is the adjacent side \( d \).
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Use trigonometric functions: With the angle given as \( 68^\circ \):
- The sine function relates the height to the length of the ladder: \[ h = L \cdot \sin(68^\circ) \]
- The cosine function relates the distance from the wall to the base of the ladder: \[ d = L \cdot \cos(68^\circ) \]
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Calculate the height and distance: If you know the length of the ladder \( L \), you can plug that value into the equations above to find \( h \) and \( d \).
For example, if \( L = 10 \) feet:
- \( h = 10 \cdot \sin(68^\circ) \)
- \( d = 10 \cdot \cos(68^\circ) \)
Using a calculator to find the sine and cosine values, you could then compute the heights and distances.
If you have specific numerical values or further details about the problem, please share, and I can assist you more directly with calculations or interpretations!