Question

The angle of elevation of top of hill from bottom of hill is 45. on walking 1000m on a hill making an angle of measure 30 with the ground, the angle of elevation of top of hill is 60 then what is height of hill.........?????

Answer 1

1.37 km


In the above figure, BC represents the height if the mountain.


sin30=PRAP 12=PR1000 PR=500⋯(1)sin⁡30=PRAP 12=PR1000 PR=500⋯(1)


cos30=ARAP √32=AR1000 AR=500√3⋯(2)cos⁡30=ARAP 32=AR1000 AR=5003⋯(2)


tan45=CBAB 1=CBAB CB=AB⋯(3)tan⁡45=CBAB 1=CBAB CB=AB⋯(3)


tan60=CQPQ √3=CB−BQRB √3=CB−PRAB−AR √3=CB−PRCB−AR  (∵ AB=CB) √3=CB−500CB−500√3 CB√3−1500=CB−500 CB(√3−1)=1000 CB=1000√3−1 =1000(√3+1)(√3−1)√3+1) =1000(√3+1)3−1 =500(√3+1)=1366.025 m =1.37 km...


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Answer 2

Answer:

$1.37 \: \bf{km}$

Step-by-step explanation:

In the above figure, BC represents the height if the mountain.

sin30=PRAP 12

=PR1000 PR=500⋯

(1)sin⁡30=PRAP 12

=PR1000 PR=500⋯

(1)cos30=ARAP √32

=AR1000 AR=500√3⋯

(2)cos⁡30=ARAP 32

=AR1000 AR=5003⋯

(2)tan45=CBAB 1

=CBAB CB=AB⋯

(3)tan⁡45=CBAB 1

=CBAB CB=AB⋯(3)

tan60=CQPQ √3

=CB−BQRB √3

=CB−PRAB−AR √3

=CB−PRCB−AR (∵ AB=CB) √3

=CB−500CB−500√3 CB√3−1500

=CB−500 CB(√3−1)

=1000 CB

=1000√3−1

=1000(√3+1)(√3−1)√3+1)

=1000(√3+1)3−1

=500(√3+1)

=1366.025 m

=1.37 km.