Question

7 nikolas is in a mineshaft that descends into the ground at an angle of 6° below horizontal after walking 2.95 kilometers into the mineshaft how far below the surface is he? 308 m 265 m 2930 m 2770 m

Explanation:

Step1: Convert kilometers to meters

Since \(1\) kilometer \( = 1000\) meters, \(2.95\) kilometers \(=2.95\times1000 = 2950\) meters.

Step2: Use the sine function

We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 6^{\circ}\) and the hypotenuse \(h = 2950\) meters. The depth \(d\) (opposite side) is given by \(d=h\sin\theta\).
Substitute \(h = 2950\) and \(\theta = 6^{\circ}\) (and \(\sin6^{\circ}\approx0.1045\)) into the formula: \(d = 2950\times0.1045\).

$$d=2950\times0.1045=(3000 - 50)\times0.1045=3000\times0.1045-50\times0.1045=313.5- 5.225=308.275\approx308$$

Answer:

308 m