Question

A 6m 70cm high wall casts a 4m 30cm long shadow. Find the height of the wall that will cast
a shadow 6m long, with the position of the sun remaining unchanged.

Answer 1

Answer:

The height of the wall is 9m 36 cm.

Step-by-step explanation:

1st case: Let AB = 6m 70 cm= 670 cm is the height of the wall, BC = 4m 30 cm = 430 cm is the length of the shadow and theta is the angle between AC and BC.

    Now, tan(theta)=AB/BC= 670/430= 1.56  

2nd case: Since the position of the sun remain unchanged , theta also remain unchanged.

  Let, DE= x cm is the height of the new wall, EF= 6m= 600 cm is the length of the shadow of the new wall and theta is angle between DF and EF .

    Therefore, tan(theta)= DE/EF = x/600

                   ⇒ 1.56= x/600          

                   ⇒ x = 600 × 1.56 = 936

    Therefore, the height of the wall is 936 cm = 9m 36 cm.

Answer 2

Answer:

9m 36 cm

Step-by-step explanation:

AB = 6m 70 cm= 670 cm is the height of the wall

BC = 4m 30 cm = 430 cm is the length of the shadow and theta is the angle between AC and BC.

 Now

      tan (theta)=AB÷BC= 670÷430 = 1.56  

the position of the sun remain unchanged  theta also remain unchanged.

 Let

     DE= x cm  the height of the new wall

      EF= 6m= 600 cm is the length of the shadow of the new wall and theta        is angle between DF and EF

 Thereafter

        tan(theta)= ⇒ DE÷EF = X÷600

                               ⇒ 1.56 = x÷600          

                             ∴ x = 600 × 1.56 = 936

   

    ∴      the height of the wall is 936 cm = 9m 36 cm.