A little boy is flying a kite. The string of the kite makes an angle of 30 dgrees with the ground. If the height of the kite is h equals 15 m, find the length (in meters)of the string that the boy has used.
To solve this problem, we can use trigonometric functions. Since we have the height of the kite and the angle it makes with the ground, we can use the sine function.
The sine function relates the opposite side (height of the kite) with the hypotenuse (length of the string). Using the formula for the sine function:
sin(angle) = opposite/hypotenuse
We can rearrange the formula to solve for the hypotenuse:
hypotenuse = opposite / sin(angle)
Given that the height (opposite side) of the kite is h = 15 m and the angle is 30 degrees, we can substitute the values into the formula:
hypotenuse = 15 m / sin(30°)
To calculate the value of sin(30°), we can use a scientific calculator or look it up in a trigonometric table. The sine of 30 degrees is 0.5.
Therefore:
hypotenuse = 15 m / 0.5
Simplifying the expression:
hypotenuse = 30 m
So, the length of the string that the boy has used is 30 meters.