Answer:
Distance = 73 m
Step-by-step explanation:
Given that,
The length of a rectangle = 48 m
The width of a rectangle = 55 m
We need to find the diagonal distance. We can use the Pythagoras theorem to find it.
So, the required distance is equal to 73 m.
Hello,
Please, see the attached file.
Thanks.
After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.
The area of a triangle with vertices known is given by the matrix
M =
![\left[\begin{array}{ccc} x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20x_%7B1%7D%26y_%7B1%7D%261%5C%5Cx_%7B2%7D%26y_%7B2%7D%261%5C%5Cx_%7B3%7D%26y_%7B3%7D%261%5Cend%7Barray%7D%5Cright%5D%20)
Area = 1/2· | det(M) |
= 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
= 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |
Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
= 1/2· | -5·(1) - 4·(-13) - 1·(12) |
= 1/2 | 35 |
= 35/2
Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
= 1/2· | -5·(11) + 4·(-13) - 1·(2) |
= 1/2 | -109 |
<span> = 109/2</span>
The total area of the quadrilateral will be the sum of the areas of the two triangles:
A(ABCD) = A(ABC) + A(ADC)
= 35/2 + 109/2
= 72
The distance between the ground and the kite to the nearest foot is 64 ft.
<h3>What is a right angle triangle?</h3>
A right angle triangle is a triangle that has one of its sides as 90 degrees. The situation forms a right angle triangle.
Hence,
The length of the kite string is the hypotenuse side of the triangle formed.
The height between the ground and the kite is the opposite side of the triangle formed.
Therefore, using trigonometric ratio,
sin 40 = opposite / hypotenuse
sin 40 = h / 100
cross multiply
h = 100 sin 40
h = 100 × 0.64278760968
h = 64.2787609687
h = 64 ft
Therefore, the distance between the ground and the kite to the nearest foot is 64 ft.
learn more on right triangle here: brainly.com/question/27482803
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