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=48 yards
To find the area of a triangle using the formula A = 1/2 ab sin C, we need to know the measures of two sides and the included angle.
Given:
a = 6 yards
b = 12 yards
∠C = 48 degrees
First, convert the angle from degrees to radians:
∠C = 48 degrees * (π/180) = 0.84 radians
Next, substitute the given values into the formula:
A = 1/2 * 6 yards * 12 yards * sin(0.84 radians)
Calculate the sin(0.84 radians):
sin(0.84) = 0.749
Now, plug in the value of sin(0.84):
A = 1/2 * 6 yards * 12 yards * 0.749
Simplify:
A = 3 yards * 12 yards * 0.749
A = 26.964 square yards
The area of triangle ABC is approximately 26.964 square yards.