What is the area of the triangle below?
A triangle is shown. The right side is 3 feet. The bottom adjacent side is 7 feet. The bottom right interior angle is 55 degrees.
(1 point)
Responses
6.0 ft²
6.0 ft²
8.6 ft²
8.6 ft²
15.0 ft²
15.0 ft²
17.2 ft²
The formula to calculate the area of a triangle is 0.5 * base * height. In this case, we do not have the height of the triangle given directly. However, we can calculate it using the trigonometric functions since we know the length of the adjacent side and the angle.
Given that the adjacent side is 7 feet and the angle opposite to it is 55 degrees, we can calculate the height using the formula: height = adjacent side * sin(angle).
height = 7 * sin(55) = 7 * 0.819 = 5.733 feet.
Now we can calculate the area of the triangle:
Area = 0.5 * 7 * 5.733 = 20.0655 ≈ 20 ft².
Therefore, the area of the triangle is approximately 20 ft². The closest option provided is 17.2 ft².