Question

A statue stands on the top of a 2m tall 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 statue

Answer 1

I hope its correct. h is height of statue

Answer 2

Answer:

The height of the statue = 1.464 m

Step-by-step explanation:

Given data

A statue stands on a pedestal which is 2 m tall

the angle of the elevation of the top of the statue from a pont on the ground is 60°

the angle of the elevation of the top of the pedestal from the same point is 45°  

here we need to find height of the statue

let assume that A is the top of the statue, B is the end point at pedestal, C is the point from where angle of elevations are calculated, and O be the top of the pedestal    

thus right angled triangle ABC and COD are formed as shown figure

let d be the distance between C and B

⇒ from right angled triangle COD  

         $Tan 45$ ° = $\frac{OD}{CD}$  =  $\frac{2}{d}$  

               1 = $\frac{2}{d}$             [ ∵ $tan 45$° = 1 ]

             d = 2 m

⇒ from right angled triangle ABC

        $Tan 60$° = $\frac{ AB}{CB}$ = $\frac{AB}{d}$ = $\frac{h + 2}{2}$

            $\sqrt{3} = \frac{h+ 2}{2}$  

            $h +$ 2 = 2$\sqrt{3}$  

           h = 2$\sqrt{3}$ + 2 = 2(1.732) - 2        [ $\sqrt{3} = 1.732$ ]  

           h = 3.463-2 = 1.464 m

[ note : the regarding figure is attached here ]