This is a very common problem for surveyors to find distances between two objects which they cannot reach. The same principle is used to find difference in heights.
Surveyors can do this today because the newer generation of theodolites can measure distance without a prism placed at the distant object.
Here we have a triangle CRT (C=carabao, R=surveyor, T=tower) in which ∠CRT=13°25', CR=30m, RT=415m.
Since two sides and the included angle are all known, the cosine rule is useful.
If the unknown side is r, RT=c (side opposite to angle C, CR=t (side opposite to angle T, then the cosine rule gives
r²=c²+t²-2ct(cos(R)).
Calculate r² and hence r using your calculator.
a surveyor wishes to measure the distance between two objects, a carabao and a tower on the opposite side of the river. while standing at point R, he finds that the distance between the carabao is 30 meters, while the distance to the tower is 415 meters. The angle formed between them is 13 degrees and 25 minutes. how far is the carabao to the tower?
i am dealing with the applications of oblique triangles. Please help me by answering my questions. thank you very much and God bless!:)
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