Two pillars are standing on either side of a 80 m wide road. Height of one pillar is 20 m more than the height of the…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2023 · Standard
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485 Marks · March 2023 · Standard
Two pillars are standing on either side of a $80$ m wide road. Height of one pillar is $20$ m more than the height of the other pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is $60^{\circ}$, whereas that of the other pillar is $30^{\circ}$. Find the position of the point between the pillars and the height of each pillar. (Use $\sqrt{3} = 1.73$)
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Correct figure $1$ Mark Let $PQ$ and $RS$ be the pillars. $\tan 60^{\circ} = \sqrt{3} = \frac{h+20}{x} \implies h+20 = x\sqrt{3}$ (i) $\tan 30^{\circ} = \frac{1}{\sqrt{3}} = \frac{h}{80-x} \implies h\sqrt{3} = 80 - x$ (ii) Using (i) and (ii) $x = 28.65, h = 29.56$ $AP = 28.65$ m, $AR = 51.35$ m $PQ = h + 20 = 49.56$ m and $RS = 29.56$ m
