Question

question 5 points 3 if a person is standing 100 m from the bottom of a tower and the angle subtended by the top of the tower with the ground is 30°, what is the height of the tower in meters? 346.4 m 57.73 m 173.22 m 115.46 m

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the \(30^\circ\) angle is \(100\) m (distance from the person to the bottom of the tower), and the height of the tower (\(h\)) is the opposite side. We use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
So, \(\tan(30^\circ)=\frac{h}{100}\).

Step2: Solve for \(h\)

We know that \(\tan(30^\circ)=\frac{1}{\sqrt{3}}\approx0.5773\).
From \(\tan(30^\circ)=\frac{h}{100}\), we can solve for \(h\) by multiplying both sides by \(100\):
\(h = 100\times\tan(30^\circ)\)
\(h = 100\times\frac{1}{\sqrt{3}}\approx100\times0.5773 = 57.73\) m.

Answer:

57.73 m (corresponding to the option "57.73 m")