Question

Use the image to answer the question.

a triangle upper A upper B upper C; The edge upper A upper B is labeled c. The edge upper A upper C is labeled b. The edge upper B upper C is labeled a.

Jerri is surveying deer for the forestry service. She puts her observation stand at point C
. Rows of trees extend for 450 ft. in one direction from her stand (side b) and for 270 ft. in another direction (side a) to form a 40-degree angle between the rows. Jerri wants to determine the area she is surveying from her stand, but she would like the total in square yards instead of square feet. What is the total area included in her survey in square yards? Round your answer to the nearest whole number.

(1 point)
Responses

39,049 yd.2

39,049 square yards

13,016 yd.2

13,016 square yards

5,171 yd.2

5,171 square yards

4,339 yd.2

Answer 1

Area = (1/2)ab sin θ = 0.5(450)(270) sin 40° = 60,750·sin 40° ≈ 39,049.37 ft².
Convert to yd²: 39,049.37 ÷ 9 ≈ 4,338.82 ≈ 4,339 yd².

Answer: 4,339 yd².