a wire is strung between a building and the ground, making a 30-60-90 triangle as shown. the wire is attached to the ground 14 feet from the building. how far up the side of the building is the wire attached?
2007-10-17 17:38:47 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Physics
Hmmm, in a 30-60-90 triangle the ratio of the sides is 1:2: sgrt 3
with 2 being the length of the wire (in this scenario, I think, but I can't see the picture to which you're referring), 1 being the 14 feet we know about, and sqrt 3 the height up the building. So, 14 feet out, 28 feet of wire, and [14 (sqrt 3)] up the building. Not entirely sure I have that right. but I think so . . .
2007-10-17 17:47:12 · answer #1 · answered by Stalagmite 3 · 0⤊ 0⤋
Let it be attached x ft. up the building.
If the angle of the wire with the ground is 30°, then
tan 30° = x / 14
=> x = 14 tan 30°
=> x = 8 ft.
If the angle of the wire with the ground is 60°, then
tan 60° = x / 14
=> x = 14 tan 60°
=> x = 24.2 ft.
2007-10-17 17:51:15 · answer #2 · answered by Madhukar 7 · 0⤊ 0⤋
A 30/60/90 triangle is half of an equilateral triangle. The short side is half of the hypotenuse. The Pythagorean theorem gives the remaining side sqrt (2^2 -1) = sqrt (3).
2007-10-17 17:49:32 · answer #3 · answered by ancient_nerd 2 · 0⤊ 0⤋
That means that the base of the triangle is 14 feet. And of the horizontal angle is ø (which may be 30º or 60º as per the picture) then up side the distance is
= 14 cot ø = 14 cot (60º or 30º)
I hope it helps.
2007-10-17 17:53:23 · answer #4 · answered by Ehsan R 3 · 0⤊ 0⤋
Does it not occur to you that "as shown" means there's a picture attached, and that we can't see the picture? The internet isn't magic, you know.
2007-10-17 17:55:06 · answer #5 · answered by lithiumdeuteride 7 · 1⤊ 0⤋
tan(angle) = x/14
x = tan(angle)*14
x is either 8.1 ft or 24.25 ft depending on what the picture shows
2007-10-17 17:55:05 · answer #6 · answered by ivan k 5 · 0⤊ 0⤋