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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, 02:26: PM
answered-by-expert Expert Answer
 
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
Answered by Rashmi Khot | 01 Dec, 2017, 05:35: PM

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