High School

A statue, 1.6 m tall, stands on top of a pedestal. From a point on the ground, the angle of elevation to the top of the statue is 60°, and from the same point, the angle of elevation to the top of the pedestal is 45°. Find the height of the pedestal.

Answer :

  • Answer:

2.2 m

  • Step-by-step explanation:

tg60° = √3

tg60° = AB/BC

∡DCB = 45° => ΔDBC = isosceles => DB = BC = h

tg60° = (AD + DB)/BC

√3 = (1.6 + h)/h

h√3 = 1.6 + h

h√3 - h = 1.6

h(√3 - 1) = 1.6

h = 1.6/(√3 - 1)

= 1.6/0.73

≈ 2.2 m

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