ICSE Class 10 Answered

$begin mathsize 12px style straight A space flagstaff space is space placed space on space top space of space straight a space building. space The space flagstaff space and space building space subtend space equal angles space at space straight a space point space on space level space ground space which space is space 200 space straight m space away space from space the space foot space of space the space building. space If space the space height space of space the space flagstaff space is space 50 space straight m space and space the space height space of space the building space is space straight h comma space prove space that space straight h cubed space plus space 50 straight h squared space plus space left parenthesis 200 right parenthesis squared straight h space minus space left parenthesis 200 right parenthesis squared 50 space equals space 0 end style$ Please provide solution to this question

Asked by Topperlearning User | 02 Nov, 2017, 09:52: AM

Expert Answer

$begin mathsize 12px style Let space AD space be space the space flagstaff space and space CD space be space the space building. space space Assume space that space the space flagstaff space and space building space subtend space equal space angles space at space point space straight B. space Given space that space AD equals 50 space straight m comma space CD equals straight h space and space BC equals 200 space straight m Let space angle ABD equals straight theta comma space angle DBC space straight theta space space space space space Then space angle ABC equals 2 straight theta from space increment BCD tanθ equals straight h over 200 from space increment BCA tan 2 straight theta equals fraction numerator 50 plus straight h over denominator 200 end fraction rightwards double arrow fraction numerator 2 tanθ over denominator 1 minus tan squared straight theta end fraction equals fraction numerator 50 plus straight h over denominator 200 end fraction rightwards double arrow 400 tanθ equals open parentheses 50 plus straight h close parentheses left parenthesis 1 minus tan squared straight theta right parenthesis rightwards double arrow 400 cross times straight h over 200 equals open parentheses 50 plus straight h close parentheses left parenthesis 1 minus open parentheses straight h over 200 close parentheses squared right parenthesis rightwards double arrow 2 straight h equals 50 minus 50 open parentheses straight h over 200 close parentheses squared plus straight h minus straight h cubed over 200 squared rightwards double arrow straight h cubed space plus space 50 straight h squared space plus space left parenthesis 200 right parenthesis squared straight h space minus space left parenthesis 200 right parenthesis squared 50 space equals space 0 end style$