Final answer:
The area of the triangle, given the side lengths of 14 yards and 12 yards with an angle of 28 degrees between them, is calculated using the formula for the area of a triangle with sides and angle. The correct answer is 39.4 yd².
Step-by-step explanation:
The student is asking to find the area of a triangle with given side lengths of 14 yards and 12 yards, and an angle of 28° between them. To find the area of a triangle given two sides and the included angle, we can use the formula:
Area = ½ × side1 × side2 × sin(angle)
Substituting the given values:
Area = ½ × 14 yd × 12 yd × sin(28°)
Using a calculator to find the sine of 28° and then calculating the area:
Area = ½ × 14 × 12 × 0.4695
Area = 7 × 12 × 0.4695
Area = 39.4 yd² (rounded to the nearest tenth)
The correct answer for the area of the triangle to the nearest tenth is 39.4 yd², which corresponds to option B).
Questions:
Find the area of each triangle to the nearest tenth. 9). 14 yd. 12 yd. E. F. D. 28°. A) 45.3 yd². B) 39.4 yd². C) 33.7 yd². D) 40.1 yd²