A triangle has two sides measuring 8 cm and 15 cm. If the angle between them is

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

A triangle has two sides measuring 8 cm and 15 cm. If the angle between them 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 angle between the two sides. Here, the angle C = 60 degrees.
Step 3: Use the formula for the area of a triangle when two sides and the included angle are known: 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 √3/2 or approximately 0.866.
Step 6: Multiply the values: Area = 1/2 * 8 * 15 * 0.866.
Step 7: Calculate 1/2 * 8 = 4.
Step 8: Calculate 4 * 15 = 60.
Step 9: Finally, calculate 60 * 0.866 = 51.96 cm² (approximately).
Step 10: Round the area to the nearest whole number if needed, which gives approximately 52 cm².

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°) = √3/2.