Question

Find the area of triangle ABC

In triangle ABC, AB = 10, BC = 4, and angle ACB = 135 degrees.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.