Final answer:
To find the area of an oblique triangle using an angle-side-angle (ASA) configuration, use the formula Area = (1/2) × b × c × sin(A), where b and c are the sides and A is the angle between them.
Step-by-step explanation:
To find the area of an oblique triangle given two angles and the side between them (ASA), you can use the law of sines to find the measures of the remaining sides first. However, an easier method involves using the formula derived from the law of sines, which directly finds the area of a triangle given two angles and the side between them:
Area = (1/2) × b × c × sin(A)
Where A is the angle between sides b and c. First, ensure you have the measures of two angles and the included side (the side between the two angles). Next, plug in the values into the formula, making sure to use the sine of the angle. Once you have the product of half the included side and the sine of the included angle, multiply it by the length of the other side to get the area.
Let's take an example. Imagine you have a triangle with angles 45° and 60°, and the included side (b) is 10 cm. The area would be calculated as follows:
- First, use the formula: (1/2) × 10 × c × sin(45°)
- Calculate sin(45°), which is √2/2
- Multiply (1/2) × 10 × c × (√2/2)
- Finally, multiply by the length of side c (once it is found using the law of sines or the third angle)
This formula is very useful when you do not know all three sides of the triangle but still need to calculate its area.