Question

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?

Answer 1

`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`