use the formula a=1/2 ab sin C to find the area of △ABC to the nearest square yard if a=6 yards, b=12 yards, and ∠C=38 yards
To find the area of the triangle ABC, we can use the given formula:
a = 1/2 * ab * sin C
Plugging in the given values:
a = 6 yards
b = 12 yards
∠C = 38 degrees
Note that the formula for the area of a triangle uses the angle in degrees, not in yards. Therefore, let's convert 38 yards to degrees. Since 1 yard is equivalent to 3 feet, and 1 foot is equivalent to 12 inches, and the circumference of a circle is 360 degrees, we have:
38 yards = 38 * 3 feet = 114 feet
114 feet = 114 * 12 inches = 1368 inches
1368 inches = 1368/36 yards = 38 degrees
Now, we can substitute the values into the formula:
Area = 1/2 * 6 yards * 12 yards * sin(38 degrees)
Using a calculator, we can find that sine of 38 degrees is approximately 0.6157. Plugging in this value:
Area = 1/2 * 6 yards * 12 yards * 0.6157
≈ 3.6942 square yards
Therefore, the area of triangle ABC, to the nearest square yard, is approximately 3.6942 square yards.