Question 1171560
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Diagram
<img width="50%" src = "https://i.imgur.com/WPmms5J.png">
The surveyor is on the side labeled "shore 1". Point Q could be any landmark on the opposite shore such as a rock or tree.


I think your teacher made a typo and should have said "The angle having the sides PR and QR was measured to be 78.24°". The angle having sides PR and PQ is the 90 degree angle. 


Based on the diagram above, we know that,
tan(angle) = opposite/adjacent
tan(angle R) = PQ/PR
tan(78.24) = x/50
50*tan(78.24) = x
x = 50*tan(78.24)
x = 240.174013162624
x = 240.17
Make sure your calculator is in degree mode.


Answer:  The distance across the lake is approximately 240.17 feet
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