Final answer:
To find the area of a triangle given two sides and an included angle, we use the formula ½ × side1 × side2 × sin(included angle). For sides of length 7 and 9 with an included angle of 72°, the area is approximately 29.75285 cm², rounded to five significant figures.
Step-by-step explanation:
The area of a triangle can also be calculated using two sides and the included angle using the formula ½ × side1 × side2 × sin(included angle). For a triangle with sides of length 7 and 9, and an included angle of 72°, the area A is calculated as follows:
A = ½ × 7 × 9 × sin(72°)
We first convert the angle to radians if our calculator is in radian mode or use the degree mode to find the sine value directly. Assuming the sine of 72° is known or calculated:
A = ½ × 7 × 9 × 0.9511
A = 29.75285 cm² (rounded to five significant figures)
The area of the triangle in square centimeters is approximately 29.75285 cm². When stating the final answer, we must consider the precision of the given lengths. Since the lengths are given as whole numbers, we assume they have infinite significant figures for this problem. Therefore, we round the area to the precision allowed by our calculations, which is to five significant figures in this case.