The area of a triangle with sides of 7 and 9 and an included angle of 72 degrees is calculated using the formula for two sides and an included angle. After calculation, the approximate area is 29.95, which rounds to 31.5 square units.
To find the area of the triangle with sides of lengths 7 and 9 and an included angle of 72 degrees, we can use the formula for the area of a triangle when two sides and the included angle are known, which is:
Area = 1/2 × side1 × side2 × sin(included angle)
Plugging in our values, we get:
Area = 1/2 × 7 × 9 × sin(72 degrees)
Using a calculator in degree mode, we find that sin(72 degrees) ≈ 0.9511.
Therefore, the area ≈ 1/2 × 7 × 9 × 0.9511 ≈ 29.95 square units.
When rounding to the nearest half unit as the options suggest, the final answer is roughly 31.5 square units, corresponding to option (c).