A kite is being flown at a 45° angle with the ground. The length of the string between the person and the kite is 100 ft. long. How high is the kite vertically above the point at which the string is being held?

Question

(1 point)
Responses

50 ft.
50 ft.

50 Start Root 2 End Root ft.
Image with alt text: 50 Start Root 2 End Root ft.

50 Start Root 3 End Root ft.
Image with alt text: 50 Start Root 3 End Root ft.

100 ft.

Answer 1

To determine how high the kite is flying vertically above the point at which the string is being held, we can use trigonometry.

Given that the string forms a 45° angle with the ground and the length of the string (hypotenuse) is 100 ft, we can use the sine function to find the vertical height (opposite side):

\[ \text{height} = \text{hypotenuse} \times \sin(\theta) \]

Substituting the known values:

\[ \text{height} = 100 , \text{ft} \times \sin(45°) \]

Since \(\sin(45°) = \frac{\sqrt{2}}{2}\):

\[ \text{height} = 100 , \text{ft} \times \frac{\sqrt{2}}{2} = 50\sqrt{2} , \text{ft} \]

Thus, the height of the kite vertically above the point where the string is held is:

\[ 50\sqrt{2} , \text{ft} \]

So the correct response is: 50 Start Root 2 End Root ft.