Question

In the right △ABC with m∠C = 90°, m∠A = 75°, and AB = 12 cm. Find the area of △ABC.

Answer 1

The area of the triangle can be found using the formula A = 1/2 * base * height. Substitute the given values and calculate the area.

Step-by-step explanation:

To find the area of a triangle, we can use the formula A = 1/2 * base * height. In this case, the base is AB and the height is AC. Since ∠C is a right angle, AC serves as the height.

To find AC, we can use the sine of ∠A: sin(∠A) = opposite/hypotenuse, AC/AB = sin(∠A), AC = AB*sin(∠A).

Now we can substitute the given values into the formula for the area:

A = 1/2 * AB * AC = 1/2 * 12 cm * 12 cm*sin(75°).