Introduction to angles of elevation and depression

Angles of elevation and depression are important concepts in trigonometry, often used to measure heights or distances indirectly. 1. Angle of Elevation: The angle of elevation is the angle formed between the horizontal line and the line of sight when you look upward to an object. For example, if you are standing on the ground and looking at the top of a tall building, the angle between the line of sight to the top of the building and the horizontal ground is the angle of elevation. 2. Angle of Depression: The angle of depression is the angle formed between the horizontal line and the line of sight when you look downward to an object. For example, if you are standing on a cliff and looking down at a boat on the water, the angle between the line of sight to the boat and the horizontal plane at your eye level is the angle of depression. Key Points: Both angles are measured relative to the horizontal line. In real-world problems, angles of elevation and depression are often used with trigonometric ratios like sine, cosine, and tangent to calculate unknown distances or heights. Example: 1. Angle of Elevation: You are 100 meters from a tree, and the angle of elevation to the top of the tree is 30°. Using trigonometry (tangent function), you can calculate the height of the tree. 2. Angle of Depression: You are on top of a tower 50 meters high, and you see a car at an angle of depression of 25°. Using the tangent function, you can calculate the distance from the base of the tower to the car. These concepts are widely used in navigation, surveying, architecture, and other fields requiring indirect measurement of distances.