Final answer:
To find the perimeter of triangle ABC, use the sine and cosine ratios to find the lengths of sides BC and AC, respectively, and then add all three sides together. To find the area, use the formula: Area = 1/2 * base * height, where the base is side AB and the height is the distance from the opposite vertex to side AB.
Step-by-step explanation:
To find the perimeter of triangle ABC, we need to find the lengths of the other two sides. Since angle A is 60° and angle C is 45°, we can use the sine and cosine ratios to find the lengths of sides BC and AC, respectively. The sine of angle C is equal to the length of BC divided by the length of AB. Therefore, BC = AB * sin(45°). The cosine of angle A is equal to the length of AC divided by the length of AB. Therefore, AC = AB * cos(60°). Once we have the lengths of all three sides, we can find the perimeter by adding them together.
To find the area of triangle ABC, we can use the formula: Area = 1/2 * base * height, where the base is side AB and the height is the distance from the opposite vertex to side AB. To find the height, we can use the sine of angle A, which is equal to the height divided by the length of AB. Therefore, height = AB * sin(60°). Once we have the base and height, we can plug them into the formula to find the area.