Question

В трапеции одна из боковых сторон перпендикулярна основаниям и =6 дм. Меньшая диагональ перпендикулярна боковой стороне и образует с меньшим основанием угол, тангенс которого равен 0,75. Найдите другую боковую сторону и основания.( плиз, срочно )

Answer 1

Я уверена, Вы сумеете нарисовать сами. Трапецию я назвала АВСD. ВС перпенд. СД.
ВД малая диагональ.
треуг. ВСД прямоугольный. катет ВС=СД×tg=6дм×0.75=4.5дм
по т. Пифагора
ВД^2=ВС^2+СД^2=4.5^2+6^2=56.25
ВД=v56.25=7.5дм.
уг. СВД=ВДА как накрест лежащие при параллельных основаниях и секущей ВД.
из прямоугольного треуг. АВД (тк ВД перпенд. АВ)
ВД/АВ=ctg
AB=BD/ctg=BD×tg=7.5×0.75=5.625дм
по т. Пифагора АД^2=7.5^2+5.625^2=87.890625
АД=9.375

Answer 2

Task: Finding the other side lengths and bases of a trapezoid

To find the other side lengths and bases of the trapezoid, we can use the given information about the perpendicularity of the sides and the tangent of an angle formed by the smaller diagonal and the smaller base.

Let's denote the trapezoid as ABCD, where AB and CD are the bases, and AD and BC are the non-parallel sides.

Given information: - One of the non-parallel sides is perpendicular to the bases and has a length of 6 dm. - The smaller diagonal is perpendicular to one of the non-parallel sides and forms an angle with the smaller base, and the tangent of that angle is 0.75.

To find the other side lengths and bases, we can use the following steps:

1. Let's denote the length of the smaller base as x dm. 2. Since one of the non-parallel sides is perpendicular to the bases, we can use the Pythagorean theorem to find the length of the other non-parallel side, which we'll denote as y dm. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have a right triangle with sides x, y, and 6 dm. - Applying the Pythagorean theorem, we have: x^2 + y^2 = 6^2. - Simplifying the equation, we have: x^2 + y^2 = 36. This is equation

3. We are also given that the tangent of the angle formed by the smaller diagonal and the smaller base is 0.75. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is y dm, and the adjacent side is x dm. So we have: - tan(angle) = y / x = 0.75. - Rearranging the equation, we have: y = 0.75x. This is equation

To find the values of x and y, we can solve equations and simultaneously.

Let's proceed with solving the equations to find the values of x and y.