Trigonometry

Trigonometry

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It uses functions like sine, cosine, and tangent to link angles to ratios of side lengths, enabling calculations of unknown distances or angles. It’s widely applied in fields like physics, engineering, architecture, and navigation.

Angle of Elevation and Angle of Depression

Angle of Elevation 

Angle of Elevation is the angle formed between the horizontal line (eye level) and the line of sight when looking upward at an object.

Angle of Depression

Angle of Depression is the angle formed between the horizontal line and the line of sight when looking downward at an object.

The device commonly used to measure angles of elevation and angles of depression is called a clinometer (or inclinometer).

How it works:

1. A clinometer measures the angle between a line of sight (to an object) and the horizontal plane.

2. It uses a weighted string, pendulum, or digital sensor to determine the tilt relative to gravity.

Note: Both angles are measured from the observer’s horizontal reference line and are key in solving real-world problems involving heights, distances, or depths (e.g., finding the height of a building or the depth of a canyon).

Practice Questions – Trigonometry

Q1. A tower on the bank of a river is 37.8 m high. If a man of height 1.8 m observes the top of the tower from the opposite bank and the angle of elevation of the top of the tower from the opposite bank is 60⁰ then,

1. Define the angle of elevation. [1K]
2. How much taller is the tower than the man? [1U]
3. Find the width of the river. [1A]
4. Where should the man move forward or backward from the tower to form a smaller angle of elevation? [1HA]