Find the area of triangleABC with B=47.6degrees, a=3.6, and c= 9.7. Round your answer to the nearest tenth.
To find the area of triangle ABC, you can use the formula for the area of a triangle using side lengths and an included angle:
Area = (1/2) * a * c * sin(B)
In this case, you have values for side a, side c, and the included angle B. Let's substitute these values into the formula:
Area = (1/2) * 3.6 * 9.7 * sin(47.6 degrees)
To calculate sin(47.6 degrees), you can use a scientific calculator or an online calculator that has trigonometric functions.
sin(47.6 degrees) ≈ 0.7313 (rounded to four decimal places)
Now, let's plug in the values:
Area ≈ (1/2) * 3.6 * 9.7 * 0.7313
Calculating the expression:
Area ≈ 12.3356
Rounded to the nearest tenth, the area of triangle ABC is approximately 12.3.