Solving for Max Height & Side Lengths of Triangle Inclined at 24 Degrees

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SUMMARY

The discussion focuses on calculating the maximum height of a rectangle and the maximum side lengths of an isosceles triangle inclined at 24 degrees. The rectangle's maximum height is determined using the formula height = 1.32 * tan(66), resulting in 2.964 meters. For the triangle, the height from the base to the centroid is calculated as 1.4823 meters, leading to an altitude of 4.449 meters when considering the centroid's relationship to the triangle's dimensions. The final hypotenuse length is computed as approximately 4.4958 meters using the Pythagorean theorem.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Familiarity with the Pythagorean theorem.
  • Knowledge of isosceles triangle properties and centroid calculations.
  • Basic geometry involving angles and inclines.
NEXT STEPS
  • Study trigonometric identities and their applications in geometry.
  • Learn about centroid calculations for various polygon shapes.
  • Explore the implications of incline angles on stability in physics.
  • Investigate advanced applications of the Pythagorean theorem in real-world scenarios.
USEFUL FOR

Students in geometry or physics courses, engineers working with inclined structures, and anyone interested in the mathematical principles of stability and height calculations in polygons.

tachu101
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Homework Statement


Given a isosceles triangle with base 1.32 meters and other sides unknown; Given rectangle with base 1.32 meters. These polygons are on an incline of 24 degrees. What are the maximum height of the rectangle and the maximum side lengths of the triangle (not the base) without have the objects tip over.

Homework Equations


The incline angle and the center of mass at 90 degrees is what the question is asking for. So the incline (24 degrees) + (unknown angle) = 90 so right away I know that the angle must be 66 degrees. Then I think that some trig comes into play.


The Attempt at a Solution


If you take half of the rectangle (to make a triangle) you can find the height of the rectangle by doing 1.32tan66=height which would get 2.964 meters. (is this the maximum height)?

The triangle is more complicated. I did the same thing and broke the triangle in half so 1.32 becomes .66 for the base. This then goes into .66tan66= height from base to the center of mass (centroid) which comes out to 1.4823 meters .
Then I think that the length of the base to the centroid and the length from the centroid to the top of the triangle is in the relationship of 1:2. So I tripled the 1.483 to get 4.449 meters as the length of the altitude.
Finally I use the Pythag Therm to get 4.449^2+.66^2= 4.4958 meters (and I think this is the answer)
 
Physics news on Phys.org
Your method looks good. (You may want to recheck your arithmetic, looking for round-off errors.)
 

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