Question

A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of top of the statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue.

Answer 1

The height of the statue is 39.165 m or 39 m.

Step-by-step explanation:

Referring to the figure attached below, let's make some assumptions

AB = height of the building  

EC = height of the statue  

BC = 35 m = distance between the building and statue

The angle of elevation from the top of the building to the top of the statue = ∠EAD = 24°

The angle of depression of the base of the statue = ∠DAC = ∠ACB = 34°

In ΔAED, applying the trigonometric properties of a triangle, we get

tan θ = Perpendicular/Base

⇒ tan 24  =  ED/AD

⇒ 0.445  =  ED/35 ….. [since BC = AD as shown in the figure]

⇒ ED  =  0.445 *35

⇒ ED  =  15.575 m  

In ΔABC, applying the trigonometric properties of a triangle, we get

tan θ = Perpendicular/Base

⇒ tan 34  =  AB/BC

⇒ 0.674 =  AB/35

⇒ AB = 0.674 * 35  

⇒ AB  =  23.59 m  

Since AB  =  DC …. As shown in the figure

∴ The height of the statue  = ED + DC = 15.575 + 23.59 = 39.165 m ≈ 39 m

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Also View:

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Angles of elevation of the top of a tower from two points at distance of 9 m and 16 m from the base of the tower in the same side and in the same straight line with it are complementary. Find the height of the tower.

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Answer 2

Answer:

• AB - Position of the building.
• CD - Position of the statue.
• AC - Distance between the building and statue angle of elevation of the top of the statue from the top of the building is ∠DBE = 24°.

Angle of depression of the bottom of the statue from the top of the building is ∠EBC = 34° .

From the figure, AC = BE, AB = CE, AC = 35m.

In the right angle triangle BDE,

tan 24° = DE / BE

DE = BE × tan 24°

= 35 × 0.4452

DE = 15.58 -----------> EQUATION 1

In the right angle triangle EBC,

tan 34° = CE / BE

CE = BE × tan 34°

= 35 × 0.6745

CE = 23.61 ------------> EQUATION 2

Adding equations 1 and 2, we get

DE + CE = 15.58 + 23.61

CD = 39.19

∴ Height of the statue = 39.19m

Step-by-step explanation:

@GENIUS