Richard is flying a kite. The kite string makes an angle of 57 degress with the ground. If Richard is standing 100 feet from the point on the ground direcly below the kite, find the length of the kite string..
Please help!!!
Draw a right triangle, and label the bottom of it the ground. The hypotenuse of this triangle is the legnth of the kite, so the angle made the hypotenuse and the ground is 57. Richard is standing 100 ft from this location, at the vertex of the right angle of this triangle, or at the other "end" of the ground. Since we have an adjacent side to the 57 degree angle (100 ft side) and are looking for the hypotenuse, we use cosine, which is adjacent over hypotenuse. So: cos(57) = 100/x. Solving this equation by multiplying by x and then dividing by cos (57) gives us 183.6 ft. So, the length of the kite string is 183.6 ft.
Check 4-18-11,1:44pm post for solution.
Richard is flying a kite. The kite string makes an angle of 57 degress with the ground. If Richard is standing 100 feet from the point on the ground direcly below the kite, find the length of the kite string..
An airplane rises vertical 1000 feet over a horizontal distance of 5280 feet. What is the angle of elevations of the airplane path?
Well, let me see if I can fly to the rescue here!
So Richard's kite string forms an angle of 57 degrees with the ground, and he's standing 100 feet away from the point directly below the kite.
Now, if we imagine a right triangle with the kite string as the hypotenuse, the angle between the kite string and the ground is 57 degrees.
Using some trigonometry magic, we can find the length of the kite string by using the cosine function! Cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is 100 feet (the distance from Richard to the point directly below the kite), and the hypotenuse is the length of the kite string we're trying to find.
So, the equation would look like this:
cos(57 degrees) = 100 feet / length of kite string
And now we just need to do a little rearranging:
length of kite string = 100 feet / cos(57 degrees)
Using our math skills, we can use a calculator to find that the length of the kite string is approximately 191.62 feet.
So it looks like Richard needs a pretty long string to keep that kite in the air! Safe flying, Richard!
To find the length of the kite string, we can use trigonometry. We have a right triangle formed by the height of the kite (the length of the kite string), the distance from Richard to the point directly below the kite, and the angle made by the kite string with the ground.
In this triangle, the height of the kite is the opposite side, the distance from Richard to the point directly below the kite is the adjacent side, and the angle is the angle. We can use the trigonometric function called tangent to calculate the height of the kite.
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we have:
Tan(angle) = opposite / adjacent
Plugging in the values we have:
Tan(57 degrees) = height / 100 feet
To solve for the height, we can rearrange the equation:
height = 100 feet * tan(57 degrees)
Now we can calculate the length of the kite string:
length of kite string = height + 100 feet
Substituting the value of height we just calculated:
length of kite string = (100 feet * tan(57 degrees)) + 100 feet
Using a calculator, we can find the numerical value of tan(57 degrees), multiply it by 100, and add 100 feet to find the length of the kite string.