Question

В равнобедренном треугольнике abc основание ac=24см и медиана bd=5см.НАЙДИТЕ 1БОКОВЫЕ СТОРОНЫ,2СИНУС УГЛА ПРИ ОСНОВАНИИИ,3ВЫСОТУ ТРЕУГОЛЬНИКА ПРОВЕДЕННУЮ К БОКОВОЙ СТОРОНЕ!!!!

Answer 1

В равнобедренном треугольнике медиана является также биссектрисой и высотой. Медиана делит основание АС на две равные части по 12 см.
К тому же медиана-высота-биссектриса делит ΔABC на два равных треугольника: ΔABD и ΔCBD.

1) Боковые стороны найдём по теореме Пифагора:
AB² = BD² + AD² = 25 + 144 = 169
АВ = 13

2) sinA = sinC = $\frac{5}{13}$

3) Найдём площадь:

SΔABC = $\frac{5*24}{2} = 12 * 5 = 60$ см²

Эту же площадь можно выразить через боковую сторону и высоту проведенную к ней. Формула та же:

h боковая ΔABC = $\frac{60*2}{13} = \frac{120}{13} = 9 \frac{3}{13}$ см

Удачи!

Answer 2

To find the side lengths, sine of the angle at the base, and the height of an isosceles triangle, we can use the properties of such triangles.

Side Lengths:

In an isosceles triangle, the two sides opposite the equal angles are congruent. Therefore, in triangle ABC, the side lengths AB and BC are equal. Let's denote the length of AB (or BC) as x.

Sine of the Angle at the Base:

The sine of an angle in a right triangle can be found using the ratio of the length of the side opposite the angle to the hypotenuse. In triangle ABC, the angle at the base is opposite side AB (or BC), and the hypotenuse is the side AC. Therefore, we can use the sine function to find the sine of the angle at the base.

Height of the Triangle:

The height of a triangle can be found by drawing a perpendicular line from one of the vertices to the base. In triangle ABC, we can draw a perpendicular line from vertex B to side AC. Let's denote the length of this perpendicular line as h.

Now, let's solve for the unknowns using the given information.

Side Lengths:

Since triangle ABC is isosceles, we know that AB = BC. Let's denote this length as x.

Sine of the Angle at the Base:

To find the sine of the angle at the base, we need to find the ratio of the length of the side opposite the angle (which is the height of the triangle) to the hypotenuse (which is the side AC). Let's denote the sine of the angle at the base as sin(θ).

Height of the Triangle:

To find the height of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In triangle ABC, the hypotenuse is side AC, and the other two sides are AB (or BC) and the height h. Therefore, we have the equation:

AC^2 = AB^2 + h^2

Given that AC = 24 cm and BD = 5 cm, we can solve for the unknowns.

Let's summarize the given information: - Base AC = 24 cm - Median BD = 5 cm

Now, let's solve for the unknowns.

Side Lengths:

Since triangle ABC is isosceles, we know that AB = BC. Let's denote this length as x.

Sine of the Angle at the Base:

To find the sine of the angle at the base, we need to find the ratio of the length of the side opposite the angle (which is the height of the triangle) to the hypotenuse (which is the side AC). Let's denote the sine of the angle at the base as sin(θ).

Height of the Triangle:

To find the height of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In triangle ABC, the hypotenuse is side AC, and the other two sides are AB (or BC) and the height h. Therefore, we have the equation:

AC^2 = AB^2 + h^2

Given that AC = 24 cm and BD = 5 cm, we can solve for the unknowns.

Let's summarize the given information: - Base AC = 24 cm - Median BD = 5 cm

Now, let's solve for the unknowns.

Side Lengths:

Since triangle ABC is isosceles, we know that AB = BC. Let's denote this length as x.

Sine of the Angle at the Base:

To find the sine of the angle at the base, we need to find the ratio of the length of the side opposite the angle (which is the height of the triangle) to the hypotenuse (which is the side AC). Let's denote the sine of the angle at the base as sin(θ).

Height of the Triangle:

To find the height of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In triangle ABC, the hypotenuse is side AC, and the other two sides are AB (or BC) and the height h. Therefore, we have the equation:

AC^2 = AB^2 + h^2

Given that AC = 24 cm and BD = 5 cm, we can solve for the unknowns.

Let's summarize the given information: - Base AC = 24 cm - Median BD = 5 cm

Now, let's solve for the unknowns.

Side Lengths:

Since triangle ABC is isosceles, we know that AB = BC. Let's denote this length as x.

Sine of the Angle at the Base:

To find the sine of the angle at the base, we need to find the ratio of the length of the side opposite the angle (which is the height of the triangle) to the hypotenuse (which is the side AC). Let's denote the sine of the angle at the base as sin(θ).

Height of the Triangle