when a child flying a kite has let out 50 m of string the string makes an angle of 55 degrees with the ground. how high is the kite
sketch a right triangle
A = 55 degrees
c = 50
a = unknown (kite height)
sin 55 deg = a/c = a/50 = 0.8192
solve for a
25
Well, I hope that kite is worth it because it's really reaching new heights! According to my calculations, if the child has let out 50 m of string and the string forms an angle of 55 degrees with the ground, then the height of the kite can be determined using some trigonometry. Assuming a flat ground and neglecting any slack in the string, the height of the kite would be approximately 39.77 meters. So, get ready to fly high with that kite!
To find the height of the kite, we can use trigonometry.
In this case, we have a right triangle formed by the height of the kite (opposite side), the length of the string (hypotenuse), and the distance from the child to the point directly beneath the kite (adjacent side).
We can use the trigonometric function tangent (tan) to solve for the height of the kite.
Tangent of an angle is equal to the ratio of the opposite side to the adjacent side. So we can use the formula:
tan(angle) = opposite / adjacent
Given that the angle is 55 degrees and the length of the string is 50 m, we can substitute these values into the formula:
tan(55) = height / 50
Now, we can solve for the height of the kite:
height = tan(55) * 50
Using a calculator, we find that the height of the kite is approximately 73.80 meters.
To find the height of the kite, we can use trigonometry. In this case, we can use the tangent function.
The tangent of an angle is defined as the opposite side divided by the adjacent side. In this scenario, the opposite side is the height of the kite, and the adjacent side is the distance from the point on the ground to where the string is being held.
Let's call the height of the kite "h."
As given in the question, the kite has let out 50 meters of string. This is the adjacent side.
The angle between the string and the ground is 55 degrees.
Using the tangent function, we have: tangent(55) = h/50
Now we need to solve for "h." We can rearrange the equation as follows:
h = 50 * tangent(55)
Now, we can calculate the height of the kite:
h ≈ 50 * 1.428
Therefore, the height of the kite is approximately 71.4 meters.