Question

Высота ромба проведена с вершины тупого угла делит сторону пополам найдите углы ромба​

Answer 1

Пошаговое объяснение:

Проведём диагональ ВD.Получим тр-к АВD.

BH - серединный перпендикуляр, медиана и высота, значит тр-к АВD-равнобедренный, т. к

АВ=ВD

Стороны ромба равны АВ=АD, значит

тр-к АВD - равноcторонний

В равностороннем тр-ке все углы равны

<А=<АВD=<BDA=60 градусов

B ромбе противоположные углы равны:

<С=<А=60 градусов

В ромбе диагонали являются биссектрисами углов :

<АВС=<АDC=2×<ABD=2×60=120 гродусов

Ответ : 60 градусов ;60 градусов ;120 гродусов ;120 гродусов

Answer 2

Finding the Angles of a Rhombus

To find the angles of a rhombus when the height is drawn from the vertex of an obtuse angle and divides one side in half, we can use the properties of a rhombus.

A rhombus is a quadrilateral with all sides of equal length. It also has some other important properties: - The diagonals of a rhombus bisect each other at right angles. - The diagonals of a rhombus divide it into four congruent right-angled triangles.

Let's denote the rhombus as ABCD, with the height drawn from the vertex of the obtuse angle at A and dividing side BC in half.

To find the angles of the rhombus, we can focus on one of the right-angled triangles formed by the diagonals. Let's consider triangle AOB, where O is the intersection point of the diagonals.

Since the height divides side BC in half, we can denote the length of BC as 2b. Therefore, the length of AB and AC is also 2b, as all sides of a rhombus are equal.

Using the Pythagorean theorem in triangle AOB, we can find the length of AO: AO^2 = AB^2 - OB^2 AO^2 = (2b)^2 - b^2 AO^2 = 4b^2 - b^2 AO^2 = 3b^2

Now, let's find the length of OB. Since the diagonals of a rhombus bisect each other at right angles, OB is half the length of BC, which is b.

Using the Pythagorean theorem in triangle AOB, we can find the length of AO: AO^2 = AB^2 - OB^2 AO^2 = (2b)^2 - b^2 AO^2 = 4b^2 - b^2 AO^2 = 3b^2

Now, let's find the length of OB. Since the diagonals of a rhombus bisect each other at right angles, OB is half the length of BC, which is b.

Using the Pythagorean theorem in triangle AOB, we can find the length of AO: AO^2 = AB^2 - OB^2 AO^2 = (2b)^2 - b^2 AO^2 = 4b^2 - b^2 AO^2 = 3b^2

Now that we have the lengths of AO and OB, we can find the sine of angle AOB using the trigonometric identity: sin(AOB) = AO / OB sin(AOB) = √(3b^2) / b sin(AOB) = √3

Since angle AOB is one of the angles of the rhombus, we have found that sin(AOB) = √3.

To find the measure of angle AOB, we can use the inverse sine function: AOB = arcsin(√3)

Therefore, the measure of angle AOB is arcsin(√3).

Since the diagonals of a rhombus bisect each other at right angles, angle AOB is half of one of the angles of the rhombus. Therefore, the measure of one of the angles of the rhombus is (1/2) * arcsin(√3).

To find the measure of the other angles of the rhombus, we can use the fact that all angles of a rhombus are equal. Therefore, each of the other three angles of the rhombus is also (1/2) * arcsin(√3).

In summary, the angles of the rhombus, when the height is drawn from the vertex of the obtuse angle and divides one side in half, are: - One angle: (1/2) * arcsin(√3) - Other three angles: (1/2) * arcsin(√3)

Please note that the exact numerical values of the angles depend on the specific length of the side of the rhombus.

I hope this explanation helps! Let me know if you have any further questions.