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Two radio masts stand on uneven ground. A survey takes a reference point as the origin, and all…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two radio masts stand on uneven ground. A survey takes a reference point as the origin, and all distances are in metres. The top of the first mast is at and the top of the second mast is at . A straight cable joins the two tops. Find the length of the cable. Then find the difference in height of the two tops.
Need a reminder? The key ideaShow
The squared distance is . For a point on an axis, set two squared distances equal. The squares of the unknown cancel and leave a linear equation. Compare squared sides to test a right angle.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. and , in metres.
Step 1. The differences. , and .
Step 2. The length. .
Step 3. The height difference. It is the difference of the -coordinates, .
Check. The cable is longer than its height difference, , as a slanted cable must be.
Answer: the cable is long and the tops differ in height by .
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