Sally is a surveyor in the badlands in South Dakota. At point A on the south side of a deep canyon, she sights across to a fire tower on the north side of the canyon at point B. Then she moves a measured 500 feet along the south rim of the canyon to a point C on a line perpendicular to her original sight line AB. Setting up her transit again, she finds that her line of sight, CB, to the tower is 85 degrees. Correct to the nearest whole foot, how far is point C from the tower?
2007-02-03 02:15:06 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
At the end of her activities, Sally knows the length of a side adjacent to an angle she knows in a right triangle and she wants to know the hypotenus of the triangle
sohcahtoa
Cos = adjacent/hypotenus
cos 85 = 500/hyp
hyp cos 85 = 500
hyp = 500/ cos 85 = 500 / 0.087155742747658173558064270837474 = 5736.8566228349275645746125179142 feet or ...to the nearest foot 5737
2007-02-03 02:26:36 · answer #1 · answered by cato___ 7 · 0⤊ 0⤋
Point C is 5737 feet from the ttower.
Since angle a is 90 degrees and angle c is 85 degrees then angle b is 5 degrees
Since angle a is 90 degres then this is a right triangle
The sine of an angle is equal to (opposite side)/hypothenuse
The sine of angle b at 5 degrees is .087156
.087156 = 500/H
.087156 times H = 500
H = 500/.087156
H = 5736.84, rounded to 5737
Check answer at http://www.pagetutor.com/trigcalc/trig.html
2007-02-03 02:50:05 · answer #2 · answered by Husker41 7 · 0⤊ 0⤋
85° from what? North? Line AC? What?
2007-02-03 02:26:34 · answer #3 · answered by Dave 6 · 0⤊ 0⤋
Cos85=500/x
x=5736.8 rounded off to 5737feet
2007-02-03 02:27:09 · answer #4 · answered by U know who 3 · 0⤊ 0⤋