Sine laws with Oblique Triangles: The Tower of Pisa

AI Thread Summary
The discussion centers on calculating the slant height of the Leaning Tower of Pisa, which leans at an angle of 5.5° and casts a 90m shadow with a 32° angle of elevation to its top. Participants clarify that the "slant height" refers to the length of the leaning side of the triangle formed by the tower and its shadow. While the sine law can be used to find this length, it is distinct from the actual vertical height of the tower. The confusion arises from the terminology, as the slant height is not the same as the height above ground. Understanding these definitions is crucial for accurate calculations.
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Here's the question: The leaning Tower of Pisa leans toward the south at an angle of 5.5°. On one day, its shadow was 90m long, and the angle of elevation from the tip of the shadow to the top of the tower is 32°.

Determine the slant height of the tower.

How high is the tip of the tower above the ground?

Now what I couldn't get is what is the "slant height?" I did the equation using the sine law, but then realized I had just found the length of the slant, not the height. Any suggestions?
 
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The "slant height" of a triangle is the height of one of its sloping sides, in this case the side where the leaning tower of pizza is leaning towards.

So, yes the length of the slant is the "slant height". The height of the leaning tower would be different (which was what you thought it was).
 

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