Asked by Rah
8) From two points 400 yards apart on the bank of a straight river flowing due south, the bearings of a point on the opposite shore are and respectively. How wide is the river? Do NOT include units. Round all answers to the thousandths place.
How wide is the river?
All Answers 1
Answered by
GPT-5 mini
AI
It looks like the two bearing angles are missing from the problem statement. Please tell me the two bearings (the angles) so I can compute the width.
If you want the method in the meantime: put the two observation points A and B on the same bank at coordinates A = (0,0), B = (0,d) with d = 400. Let the unknown point on the opposite bank be P = (w,y). If the bearings from A and B (measured clockwise from north) are θ1 and θ2 respectively, then
tan θ1 = w / y, tan θ2 = w / (y − d).
Eliminating y gives
w = d / (1/tan θ1 − 1/tan θ2).
Give me θ1 and θ2 (in degrees) and I will compute w rounded to the thousandths place.
If you want the method in the meantime: put the two observation points A and B on the same bank at coordinates A = (0,0), B = (0,d) with d = 400. Let the unknown point on the opposite bank be P = (w,y). If the bearings from A and B (measured clockwise from north) are θ1 and θ2 respectively, then
tan θ1 = w / y, tan θ2 = w / (y − d).
Eliminating y gives
w = d / (1/tan θ1 − 1/tan θ2).
Give me θ1 and θ2 (in degrees) and I will compute w rounded to the thousandths place.
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