Heights and distances · ऊँचाई और दूरी

Find the height of a tower or how far away you are — with tan 30°, 45° and 60°.

Heights and distances games

Angle of elevation and depression उन्नयन कोण और अवनमन कोण

Angle of elevation θ: from your eye's horizontal line up to the top of an object. Angle of depression: from the horizontal line down to an object below you. For a tower of height h at distance d: tan θ = h ÷ d.

θ	30°	45°	60°
sin θ	½	1/√2	√3/2
cos θ	√3/2	1/√2	½
tan θ	1/√3	1	√3

Which ratio? Height and ground distance → tan. Height and a slanting length (ladder, kite string) → sin. √3 ≈ 1.732. Also see the trigonometry table and similar triangles.

Goes with NCERT Mathematics Class 10, Chapter Some Applications of Trigonometry. Answers are exact (in √3 form).

Print

A one-page chart to stick on the wall, and a worksheet to practise.

Heights and distances

Angle of elevation and depression उन्नयन कोण और अवनमन कोण

θ	30°	45°	60°
sin θ	½	1/√2	√3/2
cos θ	√3/2	1/√2	½
tan θ	1/√3	1	√3

kheloaurseekho.in — free charts, games and worksheets

Heights and distances — worksheet

Name: ____________________ Class: ______ Date: __________

1. From 30 m away, the angle of elevation of a tower is 60°. Height = ________

2. A 20 m ladder makes 30° with the ground. It reaches ________ up the wall

3. Define the angle of depression: ____________________

4. A kite string 100 m long makes 30° with the ground. Height of the kite = ________

5. Draw a figure: a man on a 50 m cliff sees a boat at an angle of depression of 45°:

7. How far is the boat? ________

kheloaurseekho.in — free charts, games and worksheets