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Applications of Trigonometry
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17/06/2021 11:19 am
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A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
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17/06/2021 11:25 am
Let AB be the height of statue.
D is the point on the ground from where the elevation is taken.
To Find: Height of pedestal = BC = AC - AB
From figure,
In right triangle BCD,
tan 45° = BC/CD
1 = BC/CD
BC = CD …..(1)
In right ΔACD,
tan 60° = AC/AD
√3 = (AB+BC)/CD
√3CD = 1.6 + BC
√3BC = 1.6 + BC (using equation (1)
√3BC – BC = 1.6
BC(√3-1) = 1.6
BC = 1.6/(√3-1) m
BC = 0.8(√3+1)
Thus, the height of the pedestal is 0.8(√3+1) m.