Triangulation Using Trigonometry
Triangulation is the process of pinpointing a certain object or location by taking bearings to it from two remote points.
In ancient times, it could be difficult to determine distances, especially for unreachable areas. For example, observers standing on a dock would have difficulty determining the distance to a ship. However with the application of trigonometry they were able to determine how far away the ship was.
The two observers stood at a set distance d=d1+d2 from each other. They then used their instruments to measure the angles θ1 and θ2 to the boat. Now, the tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side, in this case:
Therefore we know that d = Ltan θ1+Ltan θ2, or solving for L and simplifying, L=d⋅sin θ1⋅sin θ2sin θ1+θ2.
Click on the graph to move the boat. Drag the sliders to move the observers. Compare your reading on the y-axis to the calculated value of L.
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