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 o

Question

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 pedestal is

45°

. Find the height of the pedestal. (Use

3 = 1.73

)

$Pedestal with statue, angles of elevation 45 and 60 degrees, height h, statue 1.6 m$

[IMAGE_1]

Accepted Answer

Step 1: Let $h$ be the height of the pedestal and $x$ be the distance of the point from the base.
Step 2: From figure: $\frac{h}{x} = 	an 45° = 1 \Rightarrow x = h$
Step 3: $\frac{h + 1.6}{x} = 	an 60° = \sqrt{3} \Rightarrow h + 1.6 = \sqrt{3} \cdot h$
Step 4: $\Rightarrow h(\sqrt{3} - 1) = 1.6 \Rightarrow h = \frac{1.6}{\sqrt{3} - 1} = \frac{1.6(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)} = \frac{1.6 	imes 2.73}{2} = 0.8 	imes 2.73 = 2.184$ m

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