Question

A waterfall is 12.8 km south of a lake at a bearing of 242° How far away is the waterfall from the lake? Give your answer to 2 d.p.

Answer 1

The distance between the waterfall and the lake is approximately 13.07 km.

Step-by-step explanation:

To find the distance between the waterfall and the lake, we can use trigonometry. We will use the Law of Cosines to solve for the distance.

Given:

• Distance from the waterfall to the lake: 12.8 km
• Bearing of the waterfall from the lake: 242°

To use the Law of Cosines, we need to find the angle between the line connecting the waterfall and the lake and the line of north. We can do this by subtracting the given bearing from 360°.

Angle = 360° - 242° = 118°

Now, we can use the Law of Cosines to find the distance:

d² = (12.8 km)² + (12.8 km)² - 2(12.8 km)(12.8 km)cos(118°)

d ≈ 13.07 km

Therefore, the distance between the waterfall and the lake is approximately 13.07 km.