## A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53

Question

A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. Find the area of the park to the nearest square foot.

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1. Two adjacent sides of the park say x and y are,
x=533feet
y=525feet
A=53u00ba
area=1/2*b*c*sin(A)
111739 feet^2

The area of the park is 1,11,739 square feet.

Step-by-step explanation:

Since, the area of a triangle is,

[tex]A=frac{1}{2}times s_1times s_2times sintheta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are the adjacent sides and [tex]theta[/tex] is the included angle of these sides,

Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53u00b0.

That is, [tex]s_1[/tex] = 533 ft, [tex]s_2[/tex] = 525 ft and [tex]theta[/tex] = 53u00b0,

Hence, the area of the park is,

[tex]A=frac{1}{2}times 533times 525times sin 53^{circ}[/tex]

[tex]=frac{279825times 0.79863551004}{2}[/tex]

[tex]=frac{223478.181599}{2}=111739.090799approx 111739text{ square ft}[/tex]