Base of an isosceles trapezoid = 14 and 30, sides = 10. Find the sine of the acute angle of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. AB = CD = 10 units. BC = 14 units.
AD = 30 units.
2. Let’s draw from the top B height BE to the base AD.
3. We calculate the length of the segment BE:
BE = (AD – BC) / 2 = (30 – 14) / 2 = 8 units.
4. We calculate the length of the height BE, using the Pythagorean theorem:
BE = √AB² – AE² = √10² – 8² = √100 – 64 = √36 = 6 units.
5. We calculate the sine ∠А:
Sinus ∠A = BE / AB = 6/10 = 0.6.
Answer: sine ∠A = 0.6.