Thales

Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.

Correct result:

h2 =  1.8 m

Solution:

h1=150 cmm=150/100 m=1.5 m x1=1 m x2=1.2 m h1:x1=h2:x2  h2=h1 x2x1=1.5 1.21=95=1.8 mh_{1}=150 \ cm \rightarrow m=150 / 100 \ m=1.5 \ m \ \\ x_{1}=1 \ \text{m} \ \\ x_{2}=1.2 \ \text{m} \ \\ h_{1}:x_{1}=h_{2}:x_{2} \ \\ \ \\ h_{2}=h_{1} \cdot \ \dfrac{ x_{2} }{ x_{1} }=1.5 \cdot \ \dfrac{ 1.2 }{ 1 }=\dfrac{ 9 }{ 5 }=1.8 \ \text{m}



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