Question

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30o with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (n-w = 4/3) ____________

Answer 1

Correct Answer: 50

𝑠𝑖𝑛60 = 4/3 𝑠𝑖𝑛 𝑟 
⟹ 𝑠𝑖𝑛 𝑟 = 3/4 × √3/ 2 = 3√3/8………(i)
𝑐𝑜𝑠 𝑟 = \(\sqrt{1 − 27/64}\) = √37/8 = 0.75 
⟹ 𝑡𝑎𝑛 𝑟 = \(\sqrt{27/37}\) 
⟹ 𝑥/1.5 = 0.85 
⟹ 𝑥 = 0.85 × 1.5 = 1.275𝑚 
𝑡𝑎𝑛 30 = 𝑦/2.15−1.275 =0.50
𝑦=0.875/1.732 = 0.50
So length of pole above water surface = 0.50m=50cm