Question

a tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below. how long is the tunnel? 100√3 feet 300 feet 200√3 feet 600 feet

Explanation:

Step1: Identify the trigonometric relationship

We know that in a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the depth of the tunnel (300 feet) is the opposite side to the \(30^{\circ}\) angle, and the length of the tunnel (\(L\)) is the hypotenuse. So, \(\sin30^{\circ}=\frac{300}{L}\).

Step2: Solve for \(L\)

Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{300}{L}\). Cross - multiplying gives \(L = 300\times2=600\) feet.

Answer:

600 feet