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Mr. Greenjeans wants to make a triangle shaped garden. Two sides of the garden are 52 meters and 90 meters. The angle between these two sides is 102º. What is the area of the garden?

1 Answer

2 votes

Answer:


Area = 2288.754m^2

Explanation:

The given parameters can be represented as:


A = 52m


B=90m


\theta = 102^(\circ)

Required

Determine the area of the garden

Provided that
\theta is between A and B, the area is:


Area = (1)/(2)AB sin(\theta)

Substitute values for A, B and
\theta


Area = (1)/(2)AB sin(\theta)


Area = (1)/(2) * 52 * 90 * sin(102)


Area = (1)/(2) * 52 * 90 * 0.9781


Area = (52 * 90 * 0.9781)/(2)


Area = (4577.508)/(2)


Area = 2288.754

Hence, the area of the garden is
2288.754m^2

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