Question

What is the area of △ ABC given ∠b = 115°, a = 8 feet, and c = 13 feet?

a) 47.13 feet²
b) 218.64 feet²
c) 181.37 feet²
d) 19.50 feet²

Answer 1

The area of △ ABC is approximately 47.13 square feet.

Step-by-step explanation:

To find the area of a triangle, we can use the formula A = 1/2 * base * height. In this case, the given values are angle b = 115°, side a = 8 feet, and side c = 13 feet. However, we don't have the height of the triangle. To find the height, we can use the Law of Sines:

height = sin(b) * c

Substituting the values, we get

height = sin(115°) * 13

Finally, we can substitute the base and height values into the area formula:

A = 1/2 * 8 * (sin(115°) * 13)

Simplifying the expression, the area of △ ABC is approximately 47.13 square feet.