At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 15. On walking 138 metres towards the monument the secant of the angle elevation is found to be 19312. The height of the monument (in metre) is

Given that,Distance walked towards the monument = 138mAB is the monument with height =h mDC=138 m BD=x mtan α=15 sec β=19312 We have to find the height of the monument.⇒tan β=sec2β-1 ⇒tan β=193122-1⇒tan β=193-144144⇒tan β=49144⇒tan β=712In △ABC,tan α=ABBC 15=hx+138⇒5h=x+138.... 1In △ABD,tanβ=hx ⇒712=hx ⇒x=12h7From equation 1 we get,⇒5h=12h7+138 ⇒35h-12h=138×7⇒23h=138×7 ⇒h=138×723⇒h=42m Thus, the height of the monument is 42m.Therefore, the correct option is 3.

At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 15. On walking 138 metres towards the monument the secant of the angle elevation is found to be 19312. The height of the monument (in metre) is

Given that,Distance walked towards the monument = 138mAB is the monument with height =h mDC=138 m BD=x mtan α=15 sec β=19312 We have to find the height of the monument.⇒tan β=sec2β-1 ⇒tan β=193122-1⇒tan β=193-144144⇒tan β=49144⇒tan β=712In △ABC,tan α=ABBC 15=hx+138⇒5h=x+138.... 1In △ABD,tanβ=hx ⇒712=hx ⇒x=12h7From equation 1 we get,⇒5h=12h7+138 ⇒35h-12h=138×7⇒23h=138×7 ⇒h=138×723⇒h=42m Thus, the height of the monument is 42m.Therefore, the correct option is 3.