Art Integration in Application of Trigonometry | Maths Activity | Class X

📍 Art Integration in Application of Trigonometry

Activity for Internal Assessment

[5 Marks]

Class X

Doubt by Saumya

⭐Choose any question related to application of trigonometry.

⭐Represent the given situation geometrically.

⭐Marks will be awarded considering the following : 
💡 Matching of Representation and the taken situation
💡 Imagination
💡 Artistic approach

Some Examples : 

Question : 

The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60°. Find the height of the cloud.

Solution : 
Let the height of the cloud be h m

EF=CB = 60m

FB=EC = x m

BD=(h+60) m

AB=(h-60) m

In Rt. ΔABF
tan30° = (h-60)/x

1/√3 = (h-60)/x

x=(h-60)√3 — (1)

In Rt. ΔDBF
tan60° = (h+60)/x

√3 = (h+60)/x

x√3=h+60
[(h-60)√3]√3=h+60 [∵ From eq (1)]
3h-180=h+60
3h-h=60+180
2h=240
h=240/h
h=120 m

Hence, height of the cloud from the surface of lake is 120 m.

Illustriation by Saumya Gupta of Class X