Woodpecker's Height: Solving an Angle of Elevation Problem

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SUMMARY

The discussion focuses on solving a trigonometric problem involving the height of a woodpecker in a tree, using angles of elevation. Matt observes the bird at an initial angle of elevation of 26 degrees from a distance of 20 feet, and after moving closer, he sees it at an angle of 40 degrees. The equations derived from the tangent function, tan(26) = h/(20+x) and tan(40) = h/x, allow for the calculation of the bird's height by solving these two equations simultaneously.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Ability to solve systems of equations.
  • Familiarity with angles of elevation and their applications.
  • Basic knowledge of geometry related to right triangles.
NEXT STEPS
  • Study the properties of tangent functions in trigonometry.
  • Learn how to solve systems of linear equations using substitution and elimination methods.
  • Explore real-world applications of angles of elevation in surveying.
  • Practice similar problems involving angles of elevation and distances.
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Students studying trigonometry, educators teaching geometry, and anyone interested in applying mathematical concepts to real-world problems involving angles and distances.

AstrophysicsX
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Homework Statement


Matt spies a woodpecker on the branch of a tree in a park. From the ground, the angle of elevation along his line of sight to the bird is 26 degrees. He walks 20 ft towards the tree, and in the same plane as before, now sees the bird at an angle of elevation of 40 degrees. How high in the tree is the bird?


Homework Equations


tanx = opp/adj


The Attempt at a Solution


tan26=h/20+x and tan40=h/x
 
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AstrophysicsX said:

Homework Statement


Matt spies a woodpecker on the branch of a tree in a park. From the ground, the angle of elevation along his line of sight to the bird is 26 degrees. He walks 20 ft towards the tree, and in the same plane as before, now sees the bird at an angle of elevation of 40 degrees. How high in the tree is the bird?


Homework Equations


tanx = opp/adj


The Attempt at a Solution


tan26=h/20+x and tan40=h/x

You have two equations in two unknowns. Solve for one variable in one of the equations, and substitute into the other equation. That will give you an equation with just one unknown, which you can solve for that unknown.
 

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