A radio transmission tower is 190 ft tall. How long should a guy wire be if it is attached 13 ft from the top to make an angle of 31 degrees with the ground?
2007-03-31 15:45:28 · 3 answers · asked by caydencecrabtree 1 in Science & Mathematics ➔ Mathematics
The guy wire is the hypotenuse of a right triangle whose base angle is 31 degrees. The side "opposite" the 31-degree angle is 177 feet, so use the sine of 31 to find the hypotenuse.
Rebkos, below, has something seriously wrong with her division. The sine of 31 degrees is very close to 1/2, so the wire is very close to 2 * 177, or around 354.
2007-03-31 15:48:51 · answer #1 · answered by ? 6 · 0⤊ 0⤋
The angle of 31 degrees is at the ground.
The base of the tower makes a right angle with the ground.
The wire is the hypothenuse.
The side of the triangle facing the 31 degree (the 'opposite' side) is 190 - 13.
opposite / hypothenuse = Sin(angle)
You seek the hypothenuse:
hypothenuse = opposite / Sin(31)
2007-03-31 22:50:32 · answer #2 · answered by Raymond 7 · 0⤊ 0⤋
13 feet from the top means that the height it needs to reach is 177 ft.
the sin of 31 degrees equals the length of the side opposite from the angle over the hypoteninus (which is the length you want)
sin(31) = 177/h
h= 177/sin(31)
h = 91.162
2007-03-31 22:50:13 · answer #3 · answered by rebkos 3 · 0⤊ 0⤋