1.

A statue stands on the top of a 2m tall pedestal. From a point on the ground, the angleof elevation of the top of the statue is 60% and from the same point, the angle of elevationof the top of the pedestal is 45°. Find the height of the statue.​

Answer»

Answer

  • The height of the statue will be 2(√3-1) m

Exolanation

Given

  • Length of the statue on a pedestal = 2 m
  • Angle of elevation of the top of the statue from the GROUND = 60° from the same point
  • Angle of elevation of the top of the pedestal = 45°

To Find

  • The height of the statue.

Solution

We are given with,

  1. Angle ABC = 60°
  2. Angle DBC = 45°

We know that,

➝ DC = BC = 2 m

In TRIANGLE DBC,

➝ tan 45° = DC/BC

➝ 1 = 2/BC

➝ BC = 1 × 2 = 2 m

Let 'h' be the height of the statue.

In triangle ABC,

➝ tan 60° = AC/BC

➝ √3 = AD+DC/BC

➝ √3 = h+2/2

➝ 2√3 = h + 2

➝ h = 2√3 - 2

➝ h = 2(√3-1)

Therefore, the height of the statue is 2(√3-1)


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