ICSE Class 10 Answered

$begin mathsize 12px style space When space the space sun apostrophe straight s space altitude space changes space from space 30 degree space to space 60 degree comma space the space length space of space the space shadow space of space straight a space tower space decreases space by space 70 space straight m. space What space is space the space height space of space the space tower ? end style$ Please provide solution to this question

Asked by Topperlearning User | 02 Nov, 2017, 09:59: AM

Expert Answer

$begin mathsize 12px style Let space AD space be space the space tower comma space BD space be space the space initial space shadow space and space CD space be space the space final space shadow Given space that space BC space equals space 70 space straight m comma space angle space ABD equals 30 degree angle space ACD equals 60 degree Let space CD equals space straight x space space space space AD equals space straight h space space From space the space right space increment CDA space space space tan space 60 space degree space equals fraction numerator straight h space over denominator straight x end fraction space space rightwards double arrow straight h equals straight x square root of 3 space space From space the space right space space increment BDA space space tan space 30 space degree space equals space fraction numerator straight h over denominator straight x plus 70 end fraction rightwards double arrow straight x plus 70 equals square root of 3 straight h rightwards double arrow straight x plus 70 equals 3 straight x rightwards double arrow straight x equals 35 straight h equals 35 square root of 3 space straight m end style$