Parallel Surveyor
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a triangle word problem i am stuck on?
Two markers A and B on the same side of a canyon rim are 80 ft. apart. A hiker is located on the other rim at point C. A surveyor determines that angle BAC =70 degrees and angle ABC =65 degrees.
a) What is the distance between the hiker and point A?
b) What is the distance between the two canyon rims? (Assume they are parallel)
a)
the total angles in a triangle equal 180 degrees so angle BCA= 180 - 70 - 65 = 45
now you know line AB which is opposite of angle BCA, and you know angle ABC which is opposite of line AC. to find line AC you use the sine law:
line AB/sin angle BCA = line AC/sin angle ABC
(80ft)/sin(45 degrees) = AC/sin(65 degrees)
51.3 ft = AC
b)
this would be a right angle triangle. line AC would be the hypotenuse, you know angle BAC = 70 degrees, so you use SOHCAHTOA to find the side opposite of angle BAC using:
sinBAC=opposite / hypotenuse
opposite = AC*sinBAC = (51.3ft)sin(70degrees) = 48.2ft
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June 19th, 2010 in
Dental Supplies