Answer :
The area of a triangle with sides of length 12 and 25 and an included angle of 66 degrees is approximately 136.5 square units, calculated using the formula A = 1/2 * b * c * sin(A) . The area of the triangle is approximately 136.5 square units.
To find the area of a triangle with sides of length 12 and 25, and an included angle of 66 degrees, we can use the formula for the area when two sides and the included angle are known:
A = rac{1}{2} imes b imes c imes ext{sin}(A)
where b and c are the lengths of the two sides, and A is the included angle between them. Substituting the given values, we get:
A = rac{1}{2} imes 12 imes 25 imes ext{sin}(66^{ extdegree})
To complete this calculation, we can use a calculator to find that:
ext{sin}(66^{ extdegree}) hickapprox 0.9135
Therefore, the area A hickapprox rac{1}{2} imes 12 imes 25 imes 0.9135
A hickapprox 136.5
The area of the triangle is approximately 136.5 square units.
