Igor is flying a kite. The kite is 170m off of the ground. The string of the kite and the line parallel to the ground form an angle of 68 degrees. Igor is holding the kite 1 m off of the ground. Approximately how much string has Igor let out?
looks like you are involving hypotenuse and opposite, so sine.
sin 68° = 169/string
string = 169/sin68 = ....
sin68°= 170/x
x=170/sin68°
x=183.4
Igor has let out 183.4m or 183m of string.
To find out approximately how much string Igor has let out, we can use trigonometry.
The given information tells us that the kite is 170m off the ground and that the string of the kite and the line parallel to the ground form an angle of 68 degrees.
Since we know the height of the kite (170m), and we want to find the length of the string, we can use the sine ratio.
The sine ratio is defined as the opposite side divided by the hypotenuse (in this case, the height of the kite). So in this case, we have:
sin(68 degrees) = opposite / hypotenuse
sin(68 degrees) = string / 170
To solve for the length of the string, we can rearrange the equation:
string = sin(68 degrees) * 170
Using a calculator, we can find that sin(68 degrees) is approximately 0.927.
Plugging this value into the equation, we get:
string = 0.927 * 170 ≈ 157.29
Therefore, approximately, Igor has let out around 157.29 meters of string.
To determine the length of the string Igor has let out, we need to find the length of the hypotenuse of the right triangle formed by the height of the kite from the ground and the length of the string.
We know that the height of the building is 170m and the height above the ground where Igor is holding the kite is 1m. We also know that the angle between the string and the ground is 68 degrees.
Using trigonometry, we can use the sine function to find the length of the string. The sine function relates the opposite side of an angle to the hypotenuse:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the building (170m) and the hypotenuse is the length of the string. We can rearrange the formula to solve for the hypotenuse:
hypotenuse = opposite / sin(angle)
hypotenuse = 170m / sin(68 degrees)
To calculate this using a calculator, make sure it's set to degrees mode, and then find the sine of 68 degrees. Finally, divide 170m by the sine of 68 degrees to get the length of the string Igor has let out.