The bases of an isosceles trapezoid are equal to 114 and 186. The height of the trapezoid is 45.
| August 15, 2021 | education
The bases of an isosceles trapezoid are equal to 114 and 186. The height of the trapezoid is 45. Find the cotangent of the acute angle of the trapezoid.
Since, by condition, the trapezoid ABCD is isosceles, its height BH divides the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid.
AH = (AD – BC) / 2 = (186 – 114) / 2 = 36 cm.
Since BH is the height of the trapezoid, the triangle ABH is rectangular.
In a right-angled triangle, the cotangent of its acute angle is equal to the ratio of the length of the adjacent leg to the length of the opposite leg.
CtgBAD = AH / BH = 36/45 = 0.8.
Answer: The cotangent of the acute angle of the trapezoid is 0.8.
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