Ken has let 100m of string out while flying his kite. He estimates to angle of the string to the ground is 65 degree. How high is the kite?
h/100 = sin 65°
To find the height of the kite, we can use trigonometry. In this case, the angle of the string to the ground gives us a right triangle with the string being the hypotenuse and the height of the kite being one of the legs.
Let's assume the height of the kite is "h". The hypotenuse (string length) is given as 100 meters, and the angle between the string and the ground is 65 degrees.
We can use the trigonometric function sine to find the height of the kite. The sine function relates the length of the side opposite the angle (height) to the hypotenuse:
sin(angle) = opposite/hypotenuse
So, in this case, we have:
sin(65 degrees) = h/100 meters
To find the value of sin(65 degrees), we can use a scientific calculator or an online calculator. Doing so, we find that sin(65 degrees) is approximately 0.9063.
Now, let's rearrange the equation:
h/100 meters = 0.9063
To solve for h, we can multiply both sides of the equation by 100 meters:
h = 0.9063 * 100 meters
Calculating this, we find:
h = 90.63 meters
Therefore, the estimated height of the kite is approximately 90.63 meters.