Seemingly simple arc length problem I keep getting wrong

AI Thread Summary
The problem involves calculating the distance to a plateau that is 60 meters high with a 25-degree angle of elevation. The initial approach incorrectly applies arc length concepts instead of focusing on the right triangle formed by the height and distance. The correct method involves using the sine function, where the distance to the plateau is interpreted as the adjacent side of the triangle. The accurate calculation reveals that the distance is approximately 128.67 meters, clarifying the misunderstanding around the use of arc length in this context. Understanding the geometry of the situation is crucial for solving the problem correctly.
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Homework Statement



Suppose you are headed toward a plateau 60 m high. If the angle of elevation to the top of the plateau is 25*, how far away from the plateau are you in meters?

Homework Equations



S = (theta)r

The Attempt at a Solution



In my head this translates as I am given theta and arc length and must find radius.

Radius = (arc length) / (angle measure)

25* is roughly 0.436332313 radians, 60 divided by that is roughly 137.51.

The correct answer is 128.67.

Why?
 
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i think you want to use
sin(t) = opposite/hypotenuse

draw a picture to understand why
 
Why are you talking about "arclength" at all? There is no arc or circle in this problem. You have a right triangle with one angle of 25 degrees and one leg of length 60.

I would interpret "distance to the plateau" as meaning on the flat- the "near side" of this triangle, not the hypotenuse as lanedance seems to be doing.
 
Fair bump as usual halls;)
 
Well darn, it was given among a bunch of arc length problems so i just assumed.
 

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