CBSE Class 10 Answered
The angle of elevation Φ of the top of a lighthouse as seen by a person on the ground is such that tanΦ = 5/12. When the person moves a distance of 240m towards the lighthouse, the angle of elevation becomes Φ, such that tanΦ=3/4.
Find the height of the lighthouse.
Asked by pdcavita | 19 Nov, 2017, 14:26: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/ee7ccc2e1d543c356aaced8001d063ea5a1255864d6587.61490685Nov204.png)
![begin mathsize 16px style Let space theheight space of space lighthouse space be space AB equals straight h space straight m
It space is space given space that
tan space straight alpha equals 5 over 12 space and space tan space straight beta equals 3 over 4
In space triangle CAB comma
tan space straight alpha equals AB over AC
rightwards double arrow 5 over 12 equals fraction numerator straight h over denominator 240 plus straight x end fraction..... space left parenthesis straight i right parenthesis
In space triangle DAB comma
tan space straight beta equals AB over AD
rightwards double arrow 3 over 4 equals straight h over straight x
rightwards double arrow straight x equals fraction numerator 4 straight h over denominator 3 end fraction
Substituting space straight x space in space left parenthesis straight i right parenthesis comma
5 over 12 equals fraction numerator straight h over denominator 240 plus begin display style fraction numerator 4 straight h over denominator 3 end fraction end style end fraction
rightwards double arrow 5 over 12 equals fraction numerator 3 straight h over denominator 720 plus 4 straight h end fraction
rightwards double arrow 3600 plus 20 straight h equals 36 straight h
rightwards double arrow 16 straight h equals 3600
rightwards double arrow straight h equals 225 space straight m end style](https://images.topperlearning.com/topper/tinymce/cache/c7180a2cf43338210037f7e7f10456a7.png)
Answered by Rashmi Khot | 01 Dec, 2017, 17:35: PM
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