Final answer:
To find the area of triangle XYZ with two sides and an included angle, use the formula (1/2) × base × height × sin(angle), and round the final result to three significant figures according to the least precise measurement used.
Step-by-step explanation:
To work out the area of triangle XYZ, you can use the formula for the area of a triangle when you know two sides and the included angle, which is (1/2) × base × height. However, when the height is not given, and an angle is involved, you can modify the formula to account for the angle by using this formula: area = (1/2) × XY × YZ × sin(angle XYZ). Since XY = 9.3 cm, YZ = 12.4 cm, and angle XYZ = 38°, the area is calculated as:
Area = (1/2) × 9.3 cm × 12.4 cm × sin(38°).
Firstly, convert the angle to radians if necessary and then find the value of sin(38°). Afterward, plug in all the values into the formula and solve for the area. The result should then be rounded to the appropriate number of significant figures as per the original measurements presented, which are to three significant figures in this case.
Remember, you need to follow the rules of significant figures when multiplying numbers. In an intermediate step, keep one or two extra significant figures to avoid rounding errors, but the final answer should be reported with the correct number of significant figures based on the least precise measurement used in the calculation.