Some Applications of Trigonometry

Some Applications of Trigonometry

Board: CBSE | Class: Class 10

Comprehensive study notes for Some Applications of Trigonometry by Ajay Yadav (Math King of Katargam). Master every concept with clear explanations, solved examples, and practice problems.

Key Concepts

Line of Sight

The line from the eye of the observer to the object being viewed is called the line of sight.

Angle of Elevation

The angle formed by the line of sight with the horizontal when the object is above the eye level. It is measured upward from the horizontal.

Angle of Depression

The angle formed by the line of sight with the horizontal when the object is below the eye level. It is measured downward from the horizontal.

Height and Distance Problems

Use trigonometric ratios to find heights of buildings, towers, mountains, or distances between objects. Draw a right triangle, identify known/unknown sides, and apply appropriate T-ratio.

Multiple Angles

When two angles of elevation/depression are given from different positions, set up two equations using tan ratios and solve simultaneously.

Important Formulas

Angle of Elevationtanθ = height/distance
Angle of Depressiontanθ = height/distance (same formula)
Two PositionsIf θ and φ are angles from distance x apart: h = (x tanθ tanφ)/(tanφ - tanθ)

Solved Examples

Example 1: A tower casts a shadow 50 m long when sun’s elevation is 60°. Find height.

Solution: tan60° = h/50 ⇒ √3 = h/50 ⇒ h = 50√3 = 86.6 m.

Example 2: From a point 100 m from a building, the angle of elevation is 45°. Find height.

Solution: tan45° = h/100 ⇒ 1 = h/100 ⇒ h = 100 m.

Example 3: The angle of elevation of a cloud from a point 60 m above lake is 30° and depression of its reflection is 60°. Find height.

Solution: Let cloud height = h. tan30 = (h-60)/d and tan60 = (h+60)/d. Solving: h = 120 m.

Practice Questions

  1. A kite is flying at a height of 60 m above ground. The string is 120 m long. Find the angle of elevation.
  2. A ladder 15 m long makes 60° with the wall. Find height of the wall.
  3. The angle of elevation of the top of a building from a point is 30°. Moving 20 m closer, it becomes 60°. Find height.
  4. From the top of a 75 m lighthouse, the angle of depression of a ship is 30°. Find distance of ship.
  5. Two poles of equal height stand opposite each other. Angles of elevation of their tops are 30° and 60°. Find ratio of their distances from the point.

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