Question

Find the area of the triangle having the given measurements.

B= 49°, a = 23 feet, c= 45 feet
Area=?
square feet (Round to the nearest whole number as needed.)

Answer 1

To calculate the area of the triangle, we need to find the missing side or angle using the Law of Sines and then use the formula for area that incorporates an angle, as we are not given the height.

Step-by-step explanation:

To find the area of the triangle with the given measurements (B = 49°, a = 23 feet, c = 45 feet), we cannot use the standard area formula (1/2 × base × height) directly because we do not have the height. Instead, we'll have to use the Law of Sines or the area formula that incorporates an angle, which is:

Area of a triangle = 1/2 × a × b × sin(C)

However, we do not have side b or angle C. We need to use the Law of Sines to find another side or angle first:

sin(B)/b = sin(C)/c

This allows us to find b or C. Once we find b or C, we can plug our values into the formula for the area of a triangle that includes an angle, and then calculate it to get the answer in square feet.