Use the formula A=12absinC to determine the area of △ABC . What is the area to the nearest square inch if a=16 inches , b=18 inches , and ∠C=43 degrees ?

Answer 1

To use the formula A=12absinC, we need to know the length of side c. Given that we only have the lengths of sides a and b, we need to use the Law of Cosines to find side c.

The Law of Cosines states that:
c² = a² + b² - 2abcosC

Substituting the given values, we have:
c² = 16² + 18² - 2(16)(18)cos(43°)

Solving this equation, we find that:
c² ≈ 324.95

Taking the square root of both sides, we get:
c ≈ 18.03 inches

Now, we can substitute all the values into the formula to find the area:
A = 12absinC
A = 12(16)(18)sin(43°)

Calculating this expression, we find:
A ≈ 231.72 square inches

Therefore, the area of triangle ABC is approximately 231.72 square inches to the nearest square inch.

Answer 2

options are:
134 inches2
134 inches squared

196 inches2
196 inches squared

105 inches2
105 inches squared

98 inches2

Answer 3

The correct option is:

196 inches2
196 inches squared