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 81 degrees. Correct to the nearest whole foot, how far is point C from the tower?
I got
4783
.
2006-09-02 11:51:02 · 4 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics
AC is perpendicular to AB, so use that as the right angle in your triangle.
AC measures 500 ft., and angle C measures 81°.
CB represents the hypotenuse of your triangle. You are given the side adjacent to the 81° angle, so use the cosine function.
cos 81° = [adj] / [hyp]
cos 81° = AC / CB
cos 81° = 500 / CB
Multiplying by CB and dividing by the cosine,
CB = 500 / cos 81°
CB = approx. 500 / 0.156434465
CB = approx. 3196.22661 feet.
To the nearest foot, C is 3196 feet from the tower.
2006-09-02 13:21:21 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The way I figure it, the tangent of 81 = the opposite side (distance to point b from point a) over the adjacent side (500 feet)
Working out the numbers the distance from a to b is 3157 feet. Using pythagryms theory, square root of ((3157*3157)+(500*500))gives 3196 feet.
Alternate is to use arcsine 9 degrees. The sine of 9 degrees divided into 500 feet again yields 3196 feet.
2006-09-02 19:08:06 · answer #2 · answered by Joseph G 3 · 0⤊ 0⤋
you have to know te equation
cos ( any angel ) = ( the adjcent ) / hypotenuse)
which is
cos 81 = ( AC ) / ( BC )
cos 81 = 500 / BC you get the cos of the 81 which is : .156
.156 * BC = 500
so BC = 500/ .156 = 3205.128....... so its nearly 3205 feet
2006-09-02 19:32:59 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I got 3196, you used trigonometry right?
cos81 = 500/d
d * cos81 = 500
2006-09-02 18:55:59 · answer #4 · answered by ? 3 · 0⤊ 0⤋