Algebra.Com's Answer #852181 by ikleyn(52777)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Two sides of a triangle are AB=34cm and AC=25cm and their included angle measure 62°.
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document.write( "Find the distance of the orthocenter to side AB.
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document.write( " In this problem, the given input data looks like is not related to the question,\r
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document.write( " so, it seems that it is unsolvable.\r
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document.write( " Perhaps, it is the reason why it remained unsolved about 5 years at this forum.\r
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document.write( " Nevertheless, the solution does exist and is quite beautiful, although not obvious, from the first glance.\r
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document.write( "So, we have a triangle ABC with the sides AB = 34 cm and AC = 25 cm.\r\n" );
document.write( "Their included angle A is 62°, so we can find the length of the third side BC\r\n" );
document.write( "opposite to angle A. Use the cosine law\r\n" );
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document.write( " BC =  =  = 31.3512096 cm.\r\n" );
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document.write( "Now, having the lengths of the three sides of triangle ABC, we can find its area,\r\n" );
document.write( "using the Heron's formula. In order for do not bother with calculations, I will use \r\n" );
document.write( "one of numerous online calculators, \r\n" );
document.write( "https://www.omnicalculator.com/math/herons-formula\r\n" );
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document.write( "It gives the area of triangle ABC\r\n" );
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document.write( " area(ABC) = 375.253 cm^2.\r\n" );
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document.write( "Other online calculators\r\n" );
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document.write( "https://www.inchcalculator.com/herons-formula-calculator/\r\n" );
document.write( "https://www.wolframalpha.com/widgets/view.jsp?id=7ac490665df1b278eb748160468147bc\r\n" );
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document.write( "give practically the same value.\r\n" );
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document.write( "Having the side lengths 'a', 'b' and 'c' of the triangle ABC, we can now \r\n" );
document.write( "to determine the radius of the circumscribed circle around triangle ABC\r\n" );
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document.write( " R =  =  = 17.7537 cm (rounded).\r\n" );
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document.write( "Now the distance from the orthocenter to the side AB is the leg of the right angled triangle,\r\n" );
document.write( "whose hypotenuse is R = 17.7537 cm and the other leg is half the length of the side AB.\r\n" );
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document.write( "So, we write\r\n" );
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document.write( " the distance from the orthocenter to the side AB =  = 5.118 cm (rounded).\r\n" );
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document.write( "ANSWER. The distance from the orthocenter to the side AB is 5.118 cm (rounded).\r\n" );
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document.write( "Thus, all the data was woven into one logical thread that led to a complete solution.\r
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document.write( "So, we can celebrate the victory.\r
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