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.
July 26, 2021 | education
| 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.
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