In the middle of town, State and Elm streets meet at an angle of 40º. A triangular pocket park between the streets stretches 100 yards along State Street and 53.2 yards along Elm Street. What formula for the area of the pocket park would you use?
I'd use law of cosines to find the third side, then use Heron's formula for the area.
To find the formula for the area of the pocket park, we can use the formula for the area of a triangle.
The formula for the area of a triangle is given by:
Area = 1/2 * base * height
In this case, the base of the triangle is the length along State Street, which is given as 100 yards. The height of the triangle is the length along Elm Street, which is given as 53.2 yards.
Plugging these values into the formula, we get:
Area = 1/2 * 100 * 53.2
Simplifying this expression, we get:
Area = 5300 square yards
Therefore, the formula for the area of the pocket park is:
Area = 5300 square yards