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From a window 15m high above the ground in a street,  the angles of elevation and depression of the top and foot of another house on the opposite side of the street are 30° and 45°, respectively.  Show that the height of the opposite house is 23.66 m. (take √3 = 1.732)
Asked by pdcavita | 19 Nov, 2017, 02:32: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style Let space the space window space be space at space straight P space at space straight a space height space of space 15 space straight m space above space the space ground. Let space CD space be space the space house space on space the space opposite space side space of space the space street. Let space the space height space of space the space house space CD equals space straight h space metres Now comma QD equals CD minus CQ equals CD minus AP equals left parenthesis straight h minus 15 right parenthesis space metres In space triangle space PQC comma tan space 45 degree equals QC over PQ rightwards double arrow 1 equals 15 over PQ rightwards double arrow PQ equals 15 space metres In space triangle space PQD comma tan space 30 degree equals QD over PQ rightwards double arrow fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator straight h minus 15 over denominator 15 end fraction rightwards double arrow straight h minus 15 equals fraction numerator 15 over denominator square root of 3 end fraction rightwards double arrow straight h equals 15 plus fraction numerator 15 over denominator square root of 3 end fraction rightwards double arrow straight h equals 15 plus 5 square root of 3 rightwards double arrow straight h equals 5 open parentheses 3 plus square root of 3 close parentheses equals 5 open parentheses 3 plus 1.732 close parentheses equals 5 cross times 4.732 equals 23.66 space metres. end style
Answered by Rashmi Khot | 01 Dec, 2017, 05:37: PM

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CBSE 10 - Maths
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