The straight string of a kite makes an angle of elevation from the ground of 60 degrees. The length of the string is 400 feet. What is the the height of the kite from the ground?
2007-01-20 12:58:00 · 7 answers · asked by anonymous 2 in Science & Mathematics ➔ Mathematics
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2007-01-20 12:58:16 · update #1
simple:
Make a triangle, let the length of the string be the hypotunese
and the height of the kite to be the opposite side.
then 60 degress will be the adjecent angle.
so basically your are trying to find the height (the opposite side)
so --> sin(60) = opposite/hypotonuese
so --> sin(60) = x/400
so --> sin(60)*400 = x
and x is ur ans.
2007-01-20 13:04:02 · answer #1 · answered by Gauss 2 · 0⤊ 0⤋
It might help if you draw a diagram as you read this:
If you take the point you're standing at, the point in the sky where the kite is, and the point in the ground directly below the kite, you'll notice that you can connect these points and make a right triangle, where the right angle is at the point on the ground underneath the kte, and the kite string is the hypotenuse.
The length of the hypotenuse is 400 feet. The angle where you are is 60 degrees. We want to find the height of the kite from the ground (call it "h"). This is just the leg of the triangle that's opposite of the 60 degree angle. We know the sine of an angle is the opposite divided by the hypotenuse, so sin(60) = h/400. This means h is 400*sin(60), which is 400*(sqrt(3)/2), or 200*sqrt(3).
Another way to solve this problem is to realize that we have a 30-60-90 right triangle. The sides of this kind of triangle are always in the ratio of x : x*sqrt(3) : 2x. Knowing that 2x = 400, we can use the ratios to find the length of the side across from the 60 degree angle, x*sqrt(3). We get the same answer this way, 200*sqrt(3).
2007-01-20 13:11:39 · answer #2 · answered by Anonymous · 0⤊ 0⤋
From the ground to the kite to the ground directly under the kite you have a 30-60-90 triangle.
The hypotenuse is the 400 foot string.
In a 30-60-90 triangle, the base is 1/2 of the hypotenuse, so the base is 200 ft.
Then, you can use the pythagorean theorem to find the last side, which is the height of the kite from the ground.
x^2+200^2=400^2
x^2+40,000=160,000
x^2=120,000
Then, you find the sqrt of 120,000
x=346.4102
Therefore, the hieght is 346.4102.
(I think this is right, but I haven't actually learned it in school, so I'm not 100% sure.)
2007-01-20 13:12:54 · answer #3 · answered by CheeseLord 3 · 0⤊ 0⤋
you can do it the classic trig way by using the sine 60 * 400 or..
you can remember that a 30-60-90 triangle has a unique proportion of 1,2, 1*the square root of 3 where 2 is the hypotenuse
so.. 400 /2 * the square root of 3 should give you the same answer.
..
2007-01-20 13:04:14 · answer #4 · answered by ca_surveyor 7 · 0⤊ 0⤋
draw a triangle.
400 is the long side the side you want is the vertical.
From trigonometry... sin60 gives the height of an object if the length of the long side is 1. To get it for your scenario it's 400sin60
sin60 = 1/2
400sin60 = 400(1/2) = 200
2007-01-20 13:02:53 · answer #5 · answered by Modus Operandi 6 · 0⤊ 1⤋
Sin oh hell (opposite/hypotenuse)
Cos another hour (adjacent/hypotenuse)
Tan of algebra (opposite/adjacent)
If you draw a diagram, you will see that you have the length of the a hypotenuse (400 feet) and the angle that is opposite the side you want, the height.
sin() = opposite /hypotenuse
sin(60) = opposite/ 400
400 sin (60) = opposite = height
2007-01-20 13:09:03 · answer #6 · answered by cato___ 7 · 0⤊ 0⤋
u could try multiplying them....
or wait! u divide 400 by 60
2007-01-20 13:00:59 · answer #7 · answered by Desi 2 · 0⤊ 3⤋