a kite has 120 m of string attached to it when it flies at an elevation of 5 degrees. How far is it above the hand holding it? ( assume that the string is taut)

Question

a kite has 120 m of string attached to it when it flies at an elevation of 5 degrees. How far is it above the hand holding it? ( assume that the string is taut)

Answer 1

sin 5 = h/120

Answer 2

sin5=h/120

h=sin5*120
h=0.0872*120
h=10.46

Answer 3

To find the distance the kite is above the hand holding it, we can use the concept of trigonometry.

We know that the length of the string attached to the kite is 120 m. Let's call this length "c".

The elevation angle of the string, relative to the ground, is given as 5 degrees. This angle is opposite to the distance we need to find. Let's call this distance "h".

Now, we can use the trigonometric ratio of tangent (tan) to find the distance above the hand.

The formula for tangent is: tan(theta) = opposite/adjacent

In this case, theta is the elevation angle (5 degrees), opposite is the distance above the hand (h), and adjacent is the length of the string (c).

So we have: tan(5 degrees) = h/120 m

To find h, we can rearrange the equation:

h = tan(5 degrees) * 120 m

Calculating this on a calculator, we get:

h ≈ 0.087 * 120 m

h ≈ 10.44 m

Therefore, the kite is approximately 10.44 meters above the hand holding it.

Answer 4

To find the distance above the hand holding the kite, we can use trigonometry. Specifically, we can use the sine function.

The sine function relates the length of the opposite side of a right triangle to the hypotenuse. In this case, the length of the string is the hypotenuse, and the distance above the hand holding the kite is the opposite side.

First, we need to find the length of the opposite side, which represents the distance above the hand holding the kite. We can use the formula:

Opposite side = Hypotenuse * sine(angle)

In this case, the hypotenuse is the length of the string, which is given as 120 meters, and the angle is 5 degrees.

Opposite side = 120 m * sine(5 degrees)

To evaluate this expression, we convert the angle from degrees to radians (since the sine function in most programming languages accepts angles in radians). We can use the formula:

angle in radians = angle in degrees * (pi / 180)

So, for 5 degrees:

angle in radians = 5 degrees * (pi / 180)

Now we can substitute the values into the formula:

Opposite side = 120 m * sine(angle in radians)

Calculating the above expression will give us the distance above the hand holding the kite.