Trigonometry Problems: Angles of Elevation and Depression
This page presents five trigonometry problems focusing on angles of elevation and depression, along with their solutions. These problems demonstrate practical applications of trigonometry in real-world scenarios.
Problem 10 involves calculating the height of a nest in a tree using the angle of elevation and distance from the tree base. The solution shows how to use the tangent function to find the unknown height.
Example: Jada stands 10 feet from a tree and observes a nest at a 55° angle of elevation. The height of the nest is calculated to be 14.3 feet using the tangent ratio.
Problem 11 combines a known building height with an angle of elevation to determine the height of a hot air balloon. This problem introduces a more complex scenario involving multiple heights and distances.
Problem 12 reverses the process, asking students to find the angle of elevation given the height of a building and the distance from its base. This problem uses the inverse tangent function to solve for the angle.
Highlight: The fire hydrant problem demonstrates how to use the arctangent (tan^-1) function to find an angle when given the opposite and adjacent sides of a right triangle.
Problem 13 introduces the concept of angle of depression in the context of a surfer on a wave. This problem shows how angle of depression can be used to calculate horizontal distance.
Vocabulary: Angle of depression is the angle formed by the horizontal line of sight and the line of sight to an object below the horizontal.
Problem 14 presents a more complex scenario involving a cell phone tower and support cables. This problem combines angle of depression with the height of the tower to determine the ground distance between support cables.
Example: A 140-foot tall cell phone tower has support cables at a 23° angle of depression. The ground distance between the cables is calculated to be 659.6 feet.
These problems provide valuable practice in applying trigonometric concepts to solve real-world problems involving heights, distances, and angles.
