In an isosceles trapezoid, the bases are 8 cm and 14 cm, the lateral side is 5 cm.
| April 4, 2021 | education
In an isosceles trapezoid, the bases are 8 cm and 14 cm, the lateral side is 5 cm. Find: a) the height of the trapezoid; b) sine of an acute angle at the base of the trapezoid.
The height ВН of the trapezoid ABCD divides the larger base into two segments, AH and DН.
AH = (AD – BC) / 2 = (14 – 8) / 2 = 6/2 = 3 cm.
In a right-angled triangle ABН, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16.
BH = 4 cm.
Determine the sine of the angle BAD.
SinVAD = ВН / AB = 4/5 = 0.8.
Answer: The height of the trapezoid is 4 cm, the sine of the acute angle is 0.8.
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