Final answer:
To find the area of thetriangle, use trignometry to calculate the height. Then, use the formula for the area of a triangle, which is one-half base times height.
Step-by-step explanation:
To find the area of a triangle, you can use the formula 1/2 x base x height. However, in this case, we don't have the height of the triangle. Instead, we have the length of one side and an angle. To find the height, we can use trigonometry. Since we know the length of the side adjacent to the angle and we have the length of the hypotenuse, we can use cosine to find the height.
Cosine of the angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is 8cm and the hypotenuse is AB which is 10cm. So, cos(50°) = 8/10. Solving for cos(50°), we get 0.643. Now we can find the height, which is the base of the triangle, by multiplying the hypotenuse by the cosine of the angle. So, height = AB x cos(50°) = 10cm x 0.643 = 6.43cm.
Now we have the base and the height of the triangle, we can calculate the area by using the formula 1/2 x base x height. Area = 1/2 x 6.43cm x 8cm = 25.72 cm². Since the question is asking for the area to the nearest whole number, the area of the triangle would be 26 cm².