Chapter 13, Problem 1QFR

To determine

To explain the distance measurement method by triangulation.

Answer to Problem 1QFR

The triangulation technique is a distance measurement method which is used to calculate the distance between the stars. In this technique a right angle triangle is constructed such that distance of one of its side is computed which cannot be measured directly.

Explanation of Solution

The triangulation technique is used for estimating the distance between the stars. In this method a right angle triangle is constructed such that distance of one of its side is computed which cannot be measured directly.

Figure 1 represents the constructed triangle to compute the unknown distance.

In Figure 1, the baseline length BC is taken as b, and the distance to be measured AB is taken as d.

From the above figure 1, $\tan \theta$ is written as

    $\begin{array}{c}\tan \theta =\frac{d}{b}\\ d=b\tan \theta \left[2\right]\end{array}$

In Figure 1, the length of AB need to be found, with baseline length BC is known. Then the length of AB can be calculated using the length of baseline and the angle at point C $\left(\theta \right)$.

Conclusion:

Therefore, the triangulation technique is a distance measurement method which is used to calculate the distance between the stars. In this technique a right angle triangle is constructed such that distance of one of its side is computed which cannot be measured directly.