Question

While exploring some rocky cliffs, you notice a lighthouse in the distance that you cannot quite reach. It would be nice to know how far away that lighthouse is, but there is no way to make a direct measurement over the uneven terrain. Luckily, you have your trusty compass and some knowledge about parallax and triangles. For the first vantage point, you start with the lighthouse directly north of you. You then pace out 120 steps (about 100metres) west. From this new spot, you measure the angle between due north and the new spot as 60 degrees. Determine the average distance to the lighthouse from the first point (Round to 1 decimal place.)

Answer 1

Answer:

57.8 metres is the average distance to the lighthouse round to 1 decimal place

Answer 2

Answer:

475.7 meters

Explanation:

From our first perspective, the lighthouse is directly lined up with our reference point (due north). We can refer to this as 0 degrees.

From our second perspective point, the lighthouse is 12 degrees from our reference point (due north). That means the difference between our first and second perspective points is also 12 degrees. So our parallax angle P = 12.

Using the equation (base/2)/[tan(P/2)], we can plug in our values (100/2)/[tan] (12/2) and find that the average distance to the lighthouse is about 475.7 meters.