A kite string is 350 meters long. The angle the string makes with the ground is 50 degrees. How far from the person holding the string is a person standing directly under the kite?
Trust yourself.
cosØ = adjacent/hypotenuse
cos 50° = x/350
350(cos50) = x
x = appr 224.98
clearly the answer key is wrong.
Did you make a sketch to see that
cos 50° = x/350 ?
solve for x
yes i need to find x .. and yes i made a sketch
my answer is 224.98m but the answer key says 94.71m ??
To find the distance from the person holding the kite string to the person standing directly under the kite, we can use trigonometry. Specifically, we can use the sine function.
1. First, let's draw a diagram to visualize the situation. Draw a right triangle with the kite at the top and the person holding the string at the bottom left corner. The string represents the hypotenuse of the triangle, and the angle between the string and the ground is 50 degrees.
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K / |
I / |
T / |
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2. Next, we need to identify the sides of the triangle. The length of the kite string (hypotenuse) is given as 350 meters. Let's label this side as 'c'. The distance from the person holding the string to the person under the kite is the vertical side (opposite side of the angle) of the triangle. Let's label this side as 'b'.
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350/ |
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/ b
3. We can use the sine function to relate the angle and sides of a right triangle: sin(angle) = opposite/hypotenuse.
In this case, sin(50 degrees) = b/350.
4. Rearrange the equation to solve for 'b' (distance from the person holding the string to the person under the kite):
b = 350 * sin(50 degrees).
5. Use a calculator or trigonometric table to find the sine of 50 degrees. The sine of 50 degrees is approximately 0.7660.
Therefore, b = 350 * 0.7660.
6. Calculate the value of 'b':
b ≈ 350 * 0.7660 = 268.1 meters.
So, the person standing directly under the kite is approximately 268.1 meters away from the person holding the kite string.