document.write( "Question 1205123: A water tower 30 m tall is located at the top of a hill. From a distance of 120 m down the hill it is observed that the angled formed between the top and base of the tower is 8°. Find the angle of inclination of the hill. \n" ); document.write( "

Algebra.Com's Answer #841766 by amarjeeth123(569) $\"\"$ $\"About$

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To find the angle of inclination of the hill, we can use trigonometric ratios. Let's denote the angle of inclination of the hill as θ.
\n" ); document.write( "The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle θ is the height of the water tower (30 m), and the side adjacent to the angle θ is the distance down the hill (120 m).
\n" ); document.write( "tan(θ) = opposite/adjacent
\n" ); document.write( "tan(θ) = 30/120
\n" ); document.write( "tan(θ) = 1/4
\n" ); document.write( "Solve for θ by taking the inverse tangent (arctan) of both sides of the equation.
\n" ); document.write( "θ = arctan(1/4)
\n" ); document.write( "Using a calculator or a trigonometric table, we can find the value of θ to be approximately 14.04°.
\n" ); document.write( "Therefore, the angle of inclination of the hill is approximately 14.04°. \n" ); document.write( "

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