Finding the Height of a Gondola Ski Lift Using Trigonometry

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SUMMARY

The discussion focuses on calculating the height of a gondola ski lift in Keystone, Colorado, which is 2830 meters long and rises at an angle of 14.6 degrees above the horizontal. The key equation used is the tangent function, where tan(θ) = opposite/adjacent. The length of the ski lift is identified as the hypotenuse of the right triangle formed, and the height can be determined using trigonometric functions.

PREREQUISITES
  • Understanding of basic trigonometry, specifically the tangent function.
  • Knowledge of right triangle properties and definitions of sides (hypotenuse, opposite, adjacent).
  • Familiarity with angle measurements in degrees.
  • Ability to apply trigonometric equations to real-world problems.
NEXT STEPS
  • Learn how to use the sine function to calculate heights in trigonometry.
  • Study the properties of right triangles and the Pythagorean theorem.
  • Explore practical applications of trigonometry in engineering and architecture.
  • Investigate the use of trigonometric functions in navigation and surveying.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and professionals in fields requiring geometric calculations, such as engineering and architecture.

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Homework Statement



the gondola ski lift at kystone, Corolrado is 2830m long. On avg, the ski lift rises 14.6 degree above the horizontal. How high is the top of the ski lift relative to the base.


Homework Equations



tan * = ha/h

The Attempt at a Solution



i just have a question would the 2830m long ski lift be the length of the side adjacent to the angle * or would it be the hypotenuse
 
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star20 said:

Homework Statement



the gondola ski lift at kystone, Corolrado is 2830m long. On avg, the ski lift rises 14.6 degree above the horizontal. How high is the top of the ski lift relative to the base.


Homework Equations



tan * = ha/h

The Attempt at a Solution



i just have a question would the 2830m long ski lift be the length of the side adjacent to the angle * or would it be the hypotenuse

hypotenuse
 


Angles are always in degrees.

Angle A + Angle B + Angle C = 180* always for ANY triangle.
 

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