Class 10 / Maths

Class 10 Maths Applications of Trigonometry Notes

Notes on heights and distances using angles of elevation and depression.

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Key points

Angle of elevation is measured upward from the horizontal line of sight.
Angle of depression is measured downward from the horizontal line of sight.
Most height and distance problems use tan theta because height and horizontal distance are involved.
Draw a clear diagram before choosing the trigonometric ratio.

Mark the observer, object, horizontal distance, height, and angle. The diagram usually forms one or two right triangles.

If the observer has a height, add it to the final height when needed.

Use tan theta when the opposite side and adjacent side are involved. Use sin theta or cos theta when the hypotenuse is given or asked.

Keep units consistent and write the final answer with units.

A pole casts a shadow of 10 m when the angle of elevation of the sun is 45 degrees. Find the height.
From a point 20 m away, the angle of elevation of a tower is 30 degrees. Write the equation for tower height.
Explain the difference between angle of elevation and angle of depression.
Why is tan theta commonly used in heights and distances?

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