To find the area of triangle ABC, we can use the formula for the area of a triangle given two sides and the included angle:
Area = (1/2) * AB * BC * sin(angle ACB)
Plugging in the values, we get:
Area = (1/2) * 10 * 4 * sin(135 degrees)
Area = (1/2) * 40 * sin(135 degrees)
Area = 20 * sin(135 degrees)
Using the trigonometric identity sin(135 degrees) = sin(180 degrees - 45 degrees) = sin(45 degrees) = sqrt(2)/2, we can find the final answer:
Area = 20 * sqrt(2)/2
Area = 10 * sqrt(2)
Area ≈ 14.14
Therefore, the area of triangle ABC is approximately 14.14 square units.
Find the area of triangle ABC
In triangle ABC, AB = 10, BC = 4, and angle ACB = 135 degrees.
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