A triangle has two sides measuring 8 cm and 15 cm. If the included angle is 60 d

A triangle has two sides measuring 8 cm and 15 cm. If the included angle is 60 degrees, what is the area of the triangle?

A triangle has two sides measuring 8 cm and 15 cm. If the included angle is 60 degrees, what is the area of the triangle?

Step 1: Identify the lengths of the two sides of the triangle. Here, side a = 8 cm and side b = 15 cm.
Step 2: Identify the included angle between the two sides. Here, the angle C = 60 degrees.
Step 3: Use the formula for the area of a triangle with two sides and the included angle: Area = 1/2 * a * b * sin(C).
Step 4: Substitute the values into the formula: Area = 1/2 * 8 * 15 * sin(60).
Step 5: Calculate sin(60). The value of sin(60) is approximately 0.866.
Step 6: Now calculate the area: Area = 1/2 * 8 * 15 * 0.866.
Step 7: First, calculate 1/2 * 8 = 4.
Step 8: Next, calculate 4 * 15 = 60.
Step 9: Finally, calculate 60 * 0.866 = 51.96 cm² (approximately).

Area of a Triangle – The area of a triangle can be calculated using the formula Area = 1/2 * a * b * sin(C), where a and b are the lengths of two sides and C is the included angle.
Trigonometric Functions – Understanding the sine function and its values for common angles, such as sin(60 degrees) = √3/2.