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Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string
makes a 25° angle with the ground and when the string makes a 45° angle with the ground? Round to the nearest tenth.
14.2 feet
17.1 feet
47.6 feet
55.2 feet

Respuesta :

Answer:

14.2

Step-by-step explanation:

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By using trigonometric relations, we will see that the difference in height is 14.2 ft.

How to find the difference in height?

Here we will have two right triangles, in both, the hypotenuses are equal to 50 ft, but in one, one of the angles measures 25° and in the other, the same angle measures 45°.

The height of the kite would be given by the opposite cathetus to these angles, then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse).

Then we can compute:

sin(25°) = h/50ft

sin(25°)*50ft = h = 21.1 ft

sin(45°) = h'/50ft

sin(45°)*50ft = 35.3 ft

The difference is:

35.36ft - 21.13ft = 14.2 ft

So the correct option is the first one.

If you want to learn more about right triangles, you can read:

https://brainly.com/question/2217700

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