A man 40 m from the foot of a tower observes the angle of elevation of the tower to be 30º. Determine the height of the tower.
A
\(\frac{40\sqrt{3}}{3}m\)
B
20 m
C
40√3 m
D
40 m
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Tan 30 = \(\frac{h}{40}\)
\(\frac{1}{\sqrt{3}}=\frac{h}{40}\)
h\(\sqrt{3}\) = 40
h = \(\frac{40}{\sqrt{3}}\)
h = \(\frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
h = \(\frac{40\sqrt{3}}{3}\)
Source: Myschool Past Questions Archive (Record #9251)