A kite string is 400 ft. long. If the kite makes an angle of 42 with the ground, what is the height of the kite?
sin 42 = h/400
To find the height of the kite, we can use the trigonometric function tangent (tan) since we know the length of the kite string and the angle it makes with the ground.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the height of the kite can be represented as the side opposite the angle, and the length of the kite string can be represented as the side adjacent to the angle.
Let's denote the height of the kite as h and the length of the kite string as l.
Using trigonometry, we have:
tan(angle) = height / length of kite string
tan(42°) = h / 400 ft
Now, we can solve for h by rearranging the equation:
h = tan(42°) * 400 ft
Using a calculator, we find:
h ≈ tan(42°) * 400 ft ≈ 312.7 ft
Therefore, the height of the kite is approximately 312.7 feet.
To find the height of the kite, we can use trigonometry, specifically the sine function. The sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the length of the string is the hypotenuse, and the height of the kite is the side opposite the angle of 42 degrees.
We can set up the equation as follows:
sin(42 degrees) = height of the kite / length of the string
Now we can solve for the height of the kite:
height of the kite = sin(42 degrees) * length of the string
height of the kite = sin(42 degrees) * 400 ft
To find the value of sin(42 degrees), you can use a scientific calculator or a trigonometric table. The sine of 42 degrees is approximately 0.669.
Therefore, the height of the kite is:
height of the kite = 0.669 * 400 ft
height of the kite ≈ 267.6 ft
The height of the kite is approximately 267.6 ft.