# 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.