Find the area of an isosceles trapezoid if its diagonal equal to 5 forms an angle of sine with the base equal to 0.6.

1. The tops of the trapezoid – A, B, C, D. СK – height. S is the area of the trapezoid. Diagonal AC = 5 units. Sinus ∠CAD = 0.6.

2. In a right-angled triangle ACK, the sine ∠САD = СK / AC.

CK = AC x 0.6 = 5 x 0.6 = 3 units.

3. AK² = AC² – СK² (by the Pythagorean theorem).

AK = √AC² – СK² = √5² – 3² = √25 – 9 = √16 = 4 units.

3. In an isosceles trapezoid, the AK segment is calculated by the formula:

AK = (BC + AD) / 2 = 4 units.

4. S = (BC + AD) / 2 x CK = 4 x 3 = 12 units of measurement².