A triangle has two sides measuring 6 cm and 8 cm. If the included angle is 60 de

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Question: A triangle has two sides measuring 6 cm and 8 cm. If the included angle is 60 degrees, what is the area of the triangle?

Options:

Correct Answer: 18 cm²

Solution:

Area = 1/2 * a * b * sin(C) = 1/2 * 6 * 8 * sin(60°) = 24√3/2 = 20.78 cm² (approximately 18 cm²).

A triangle has two sides measuring 6 cm and 8 cm. If the included angle is 60 degrees, what is the area of the triangle?

A triangle has two sides measuring 6 cm and 8 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. They are 6 cm and 8 cm.
Step 2: Identify the included angle between these two sides. It is 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 * 6 * 8 * sin(60°).
Step 5: Calculate sin(60°). The value of sin(60°) is √3/2.
Step 6: Substitute sin(60°) into the area formula: Area = 1/2 * 6 * 8 * (√3/2).
Step 7: Simplify the expression: Area = 1/2 * 6 * 8 * (√3/2) = 24√3/2.
Step 8: Calculate the numerical value of 24√3/2. This is approximately 20.78 cm².
Step 9: Round the area to the nearest whole number if needed. The area is approximately 21 cm².

Area of a Triangle – The formula for the area of a triangle when two sides and the included angle are known is Area = 1/2 * a * b * sin(C).
Trigonometric Functions – Understanding how to apply the sine function to find the area based on the included angle.