A man is flying a kite on an eighty foot string. The kite has an angle of elevation measuring fifty five
1 answer:
Answer:
45.9 feet
Step-by-step explanation:
In this situation, the kite string represents the hypotenuse of a right triangle.
We need to solve for the horizontal distance, which will be the long leg of the triangle.
Use the cosine ratio (adjacent over hypotenuse), since we are given the hypotenuse and are solving for the adjacent leg.
Let x represent the horizontal distance:
cos 55 =
(80) (cos 55) = x
45.9 = x
So, the horizontal distance is approximately 45.9 feet
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Answer:
Dimensions:
Perimiter:
Minimum perimeter: [16,16]
Step-by-step explanation:
This is a problem of optimization with constraints.
We can define the rectangle with two sides of size "a" and two sides of size "b".
The area of the rectangle can be defined then as:
This is the constraint.
To simplify and as we have only one constraint and two variables, we can express a in function of b as:
The function we want to optimize is the diameter.
We can express the diameter as:
To optimize we can derive the function and equal to zero.
The minimum perimiter happens when both sides are of size 16 (a square).