Step 1: Analyse the given information and draw a figure by using the given measurements.
NOTE: The height of the statue AB = h
Height of the pedestal BC = 2 m
The angle of elevation of the top of the statue = 60 \degree
The angle of elevation of the top of the pedestal = 45 \degree
Step 2: Find the height of the statue by using the suitable trigonometric ratios.
Height of the statue AB = AC - BC
Determine the length of the AC:
NOTE: From triangle BCP
\tan 45 \degree = \frac{opposite}{adjacent} = \frac{BC}{PC}
\tan 45 \degree = \frac{2}{PC}
1 = \frac{2}{PC} ( \because \tan 45 \degree = 1 )
PC = 2 m..............(1)
From triangle ACP
\tan 60\degree = \frac{opposite}{adjacent} = \frac{AC}{PC}
\tan 60\degree = \frac{AC}{2} (Since, equation (1))
\sqrt{3} = \frac{AC}{2} (\because\tan60\degree=\sqrt{3}
AC = 2\sqrt{3}
Height of the statue AB = AC - BC
AB = 2\sqrt{3} - 2
AB = 2(\sqrt{3} - 1)
AB = 2(1.732 - 1)
AB = 2(0.732)
AB = 1.464 m