Answer:
23.94 square units
Explanation:
To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height.
In this case, the base is the side with length 9 (side two) and the height is the line perpendicular to the base, which can be found using trigonometric functions.
Let's label the height as h. To find h, we can use the sine function:
sin(angle) = opposite/hypotenuse.
In this case, the opposite side is 7 (side one) and the hypotenuse is 9 (side two).
sin(5n/6) = 7/9.
To solve for n, we need to isolate it.
n = (6/5) * arcsin(7/9).
Now that we have n, we can substitute it into the equation for h:
h = 9 * sin(5n/6).
Finally, we can calculate the area:
Area = (1/2) * 9 * h.
Let's calculate it using the given angle:
n = (6/5) * arcsin(7/9) ≈ 0.789.
h = 9 * sin(5 * 0.789 / 6) ≈ 5.32.
Area ≈ (1/2) * 9 * 5.32 ≈ 23.94 square units.
Therefore, the area of the triangle is approximately 23.94 square units.