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
Solution:
Let the height of the pedestal be BC, the height of the statue, which stands on the top of the pedestal, be AB. D is the point on the ground from where the angles of elevation of the bottom B and the top A of the statue AB are 45° and 60° respectively.
The distance of the point of observation D from the base of the pedestal is CD. Combined height of the pedestal and statue AC = AB + BC
Trigonometric ratio involving sides AC, BC, CD, and ∠D (45° and 60°) is tan θ.
In ΔBCD,
tan 45° = BC/CD
1 = BC/CD
Thus, BC = CD
In ΔACD,
tan 60° = AC/CD
tan 60° = (AB + BC)/CD
√3 = (1.6 + BC)/BC [Since BC = CD]
√3 BC = 1.6 + BC
√3 BC - BC = 1.6
BC (√3 - 1) = 1.6
BC = 1.6 × (√3 + 1)/(√3 - 1)(√3 + 1)
= 1.6 (√3 + 1)/(3 - 1)
= 1.6 (√3 + 1)/2
= 0.8 (√3 + 1)
Height of pedestal BC = 0.8 (√3 + 1) m.
☛ Check: NCERT Solutions Class 10 Maths Chapter 9
Video Solution:
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.
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 8
Summary:
If a statue, 1.6m tall, stands on the top of a pedestal, from a point on the ground and 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°, then the height of the pedestal is 0.8(√3+1) m.
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