From a point on the ground, 30m away from the foot of a tower, the angle of elevation of the top of the…

From a point on the ground, 30m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is:

  1. \(10\text{m}\)

  2. \(10\sqrt3\text{m}\)

  3. $30\sqrt{3}\text{m}$

  4. \(30\text{m}\)

Solution

Solution:

In right triangle ABC,

\(\tan30^\circ=\frac{\text{AB}}{\text{BC}}\) 

\(\Rightarrow\frac{1}{\sqrt3}=\frac{\text{AB}}{30}\)

\(\text{AB}=\frac{30}{\sqrt3}\text{m}\)

\(\Rightarrow\frac{30}{\sqrt3}\times\frac{\sqrt3}{\sqrt3}\)

\(10\sqrt3\text{m}\)

Hence the height of the tower is \(10\sqrt3\text{ meters}.\)

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