SOLUTION: To determine the distance across a lake, a surveyor selected two points P and Q, one on each shore and directly
opposite each other. On the shore containing P, another point R was
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opposite each other. On the shore containing P, another point R was
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Question 1171560: To determine the distance across a lake, a surveyor selected two points P and Q, one on each shore and directly
opposite each other. On the shore containing P, another point R was chosen, 50 ft from P, so that the line segment PR
was perpendicular to the line segment PQ. The angle having the sides PR and PQ was measured to be 78.24°. What
is the distance across the lake? Round off your answer to two decimal places.
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Diagram
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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