Question

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?

Answer 1

the correct answer is option 2). 50√2

Explanation:

From the figure attached with this answer shows,

AB is the length of the string between the person and the kite is 100 ft. long.

Triangle ABC is a right triangle.

<A = 45°,<B = 90° and AB = 100 ft

To find height of kite

The angles are 45° , 45°, 90°

Therefore sides are in the ratio 1 : 1: √2

AC : BC : AB = 1 : 1: √2 = AC : BC : 100

Therefore AC = 100/√2 = 50√2

The correct answer is option 2). 50√2

Answer 2

Answer:
`50√(2)ft`

Explanation:

1. Draw a right triangle as the one shown in the figure attached, where the hypotenuse is 100 feet and the angle α is 45°.

2. Then, you can calculate x (the height above the point at which the string is being held) as following:

`sin\alpha=(opposite)/(hypotenuse)`

Substitute values and solve for x:

`sin\alpha=(x)/(100)\\x=100*sin(45)\\x=50√(2)`

3. Therefore, the answer is
`50√(2)ft`