In an isosceles trapezoid ABCD, the angle A is 45 degrees, the side BC is 37 cm, and the height BH
| March 2, 2021 | education
In an isosceles trapezoid ABCD, the angle A is 45 degrees, the side BC is 37 cm, and the height BH is 12 cm. How many cm is the length AB?
To find the length of the AB side, there is no need to use the data on the BC side (BC = 37 cm), in this case it is an unnecessary data.
Consider △ ABC – it is rectangular.
In a right-angled triangle, the sine of an acute angle is equal to the ratio of the opposite leg to the hypotenuse.
B △ ABC: ∠ A – acute (45o), ВН – opposite leg, AB – hypotenuse.
sin ∠ A = BH: AB.
sin 45о = ВН: AB.
12: AB = √2: 2.
AB = 12: (√2: 2).
AB = 12 x 2 / √2.
AB = 24 / √2.
Multiply the numerator and denominator of the fraction by √2:
AB = 24 x √2 / √2 x √2.
AB = 24√2 / 2.
AB = 12√2 (cm).
Answer: the length of the AB side is 12√2 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
