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.
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Correct Answer: Option A
Explanation:
\(Tan 30 = \frac{h}{40}\\
\frac{1}{\sqrt{3}}=\frac{h}{40}\\
h\sqrt{3}=40\\
h = \frac{40}{\sqrt{3}}\\
h = \frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\\
h = \frac{40\sqrt{3}}{3}\)
\(Tan 30 = \frac{h}{40}\\
\frac{1}{\sqrt{3}}=\frac{h}{40}\\
h\sqrt{3}=40\\
h = \frac{40}{\sqrt{3}}\\
h = \frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\\
h = \frac{40\sqrt{3}}{3}\)