"Published in Newark, California, USA"
The points C and D in the figure lie on level ground in the same vertical plane with the tip B of the tower AB. If the tower AB is 300 ft. high and measurements give A1B1 = 5 ft., CA1 = 12 ft., A2B2 = 6 ft., and A2D = 8 ft., find the distance CD.
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| Photo by Math Principles in Everyday Life |
Solution:
The given problem above is asking for a distance of two points which is CD using similar triangles. The tower is located between CD and assuming that it is perpendicular to the ground. In this case, there are four right triangles in the figure. Label further the figure above, we have
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| Photo by Math Principles in Everyday Life |
Consider ∆ABC:
Using similar triangles, we have
Consider ∆ABD:
Using similar triangles, we have
Therefore,
