Question

1. Известно, что tga=-5/12.Найдите sina, cosa.2.Из формулы S=1/2ab sinC выразите:a=b=c=sinC=3.В двух треугольниках основания равны, а высота одного из них в четыре раза больше. Найдите отношение площадей этих треугольников.4. Стороны треугольника равны 15см и 13 см, а угол между ними - 30градусов. Найдите площадь этого треугольника.5. Угол при основании равнобедренного треугольника равен 45 градусов, а площадь его - 9корней из 3 в квадрате. Найдите высоту треугольника.ЗАРАНЕЕ ОГРОМНОЕ СПАСИБО!!!!)))

Answer 1

1)Тангенс - это отношение синуса к косинусу , отсюда :

  sina= -5, cosa = 12

2) a = S/ 0,5b sinc

    b = S / 0,5a sin c

    sin c = S / 0,5 ab 

    А насчет с, тут надо знать чему равен синус.

3) Площадь треугольников рассчитывается по формуле: 

    S = 0,5 bh

   Где b - основание треугольника

          h - его высота.

          Площадь первого треугольника S = 0,5 b 4h

          Площадь второго треугольника S = 0,5 b h

          Соответственно, если увеличилась высота в 4 раза, то увеличится и площадь тоже в 4 раза, так как это прямопропорциональные величины . Значит , отношение треугольников - 4/1.

4) Не уверен, но по-моему вот так :

    S = 0,5 a b sinc = 0,5 15 13 0,5 = 48,75

    (sin 30 = 0,5)

5)  

 

 

 

 

 

 

 

      

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

Answer 2

1. Найдите sina и cosa, если известно, что tga = -5/12.

To find sina and cosa, we can use the trigonometric identity:

sin^2a + cos^2a = 1

Given that tga = -5/12, we can use the following trigonometric identity:

tga = sina / cosa

Rearranging the equation, we have:

cosa = sina / tga

Substituting this into the first trigonometric identity, we get:

sin^2a + (sina / tga)^2 = 1

Expanding the equation, we have:

(sin^2a * tga^2) + sina^2 = tga^2

Rearranging the equation, we get:

(1 + tga^2) * sin^2a = tga^2

Now, we can substitute tga = -5/12 into the equation:

(1 + (-5/12)^2) * sin^2a = (-5/12)^2

Simplifying the equation, we have:

(1 + 25/144) * sin^2a = 25/144

Multiplying both sides by 144, we get:

(144/144 + 25/144) * sin^2a = 25/144

Simplifying further, we have:

(169/144) * sin^2a = 25/144

Dividing both sides by 169/144, we get:

sin^2a = (25/144) / (169/144) = 25/169

Taking the square root of both sides, we get:

sin a = sqrt(25/169) = 5/13

Now, we can substitute sin a into the equation:

cosa = sina / tga = (5/13) / (-5/12) = -12/13

Therefore, sina = 5/13 and cosa = -12/13.

2. Из формулы S = 1/2ab + sinC выразите: a = b = c = sinC = ?

Given the formula S = 1/2ab + sinC, we can express a, b, c, and sinC in terms of S.

To express a, we can rearrange the formula as:

2S = ab + 2sinC

Dividing both sides by b, we get:

2S / b = a + 2sinC / b

Subtracting 2sinC / b from both sides, we get:

2S / b - 2sinC / b = a

Therefore, a = 2S / b - 2sinC / b.

Similarly, we can express b, c, and sinC as:

b = 2S / a - 2sinC / a

c = 2S / sinC - 2ab / sinC

sinC = 2(S - 1/2ab) / c

Please note that these expressions may not be simplified further and depend on the given formula S = 1/2ab + sinC.

3. Найдите отношение площадей двух треугольников, где основания равны, а высота одного из них в четыре раза больше.

Let's denote the bases of the two triangles as b1 and b2, and the heights as h1 and h2, respectively.

Given that the bases are equal (b1 = b2) and the height of one triangle is four times greater than the other (h2 = 4 * h1), we can find the ratio of their areas.

The area of a triangle is given by the formula: Area = (1/2) * base * height.

For the first triangle, the area is: Area1 = (1/2) * b1 * h1.

For the second triangle, the area is: Area2 = (1/2) * b2 * h2.

Since b1 = b2, we can simplify the formula for Area2 as: Area2 = (1/2) * b1 * (4 * h1).

Simplifying further, we have: Area2 = 2 * b1 * h1.

Now, we can calculate the ratio of the two areas: Ratio = Area2 / Area1.

Substituting the values, we get: Ratio = (2 * b1 * h1) / ((1/2) * b1 * h1).

Simplifying the expression, we have: Ratio = 4.

Therefore, the ratio of the areas of the two triangles is 4.

4. Стороны треугольника равны 15 см и 13 см, а угол между ними - 30 градусов. Найдите площадь этого треугольника.

To find the area of a triangle, we can use the formula: Area = (1/2) * base * height.

In this case, the two sides of the triangle are given as 15 cm and 13 cm, and the angle between them is 30 degrees.

To find the height, we can use the formula: height = side * sin(angle).

Substituting the values, we have: height = 15 cm * sin(30 degrees).

Using the value of sin(30 degrees) = 1/2, we can calculate the height: height = 15 cm * (1/2) = 7.5 cm.

Now, we can calculate the area of the triangle: Area = (1/2) * base * height.

Substituting the values, we have: Area = (1/2) * 13 cm * 7.5 cm.

Calculating the expression, we get: Area = 48.75 cm^2.

Therefore, the area of the triangle is 48.75 square centimeters.

5. Угол при основании равнобедренного треугольника равен 45 градусов, а площадь его - 9 корней из 3 в квадрате. Найдите высоту треугольника.

To find the height of an isosceles triangle, we can use the formula: Height = sqrt((leg^2) - ((base/2)^2)).

In this case, the angle at the base of the isosceles triangle is 45 degrees, and the area is given as 9 * sqrt(3).

Let's denote the leg of the triangle as leg and the base as base.

Since the triangle is isosceles, the two legs are equal. Therefore, we can rewrite the formula as:

Height = sqrt((leg^2) - ((base/2)^2)) = sqrt((leg^2) - (leg^2/4)) = sqrt((3/4) * leg^2) = (sqrt(3)/2) * leg.

Given that the area of the triangle is 9 * sqrt(3), we can use the formula for the area of a triangle to find the relationship between the legs and the base:

Area = (1/2) * base * height.

Substituting the values, we have: 9 * sqrt(3) = (1/2) * base * ((sqrt(3)/2) * leg).

Simplifying the equation, we get: 18 = (sqrt(3)/4) * base * leg.

Now, we can substitute the relationship between the legs and the base in terms of the leg:

18 = (sqrt(3)/4) * base * ((2 * height) / sqrt(3)).

Simplifying further, we have: 18 = (1/2) * base * height.

Substituting the values, we have: 18 = (1/2) * base * ((sqrt(3)/2) * leg).

Simplifying the equation, we get: 18 = (1/2) * base * ((sqrt(3)/2) * leg).

Now, we can substitute the relationship between the legs and the base in terms of the leg:

18 = (1/2) * base * ((sqrt(3)/2) * leg).

Simplifying further, we have: 18 = (1/2) * base * ((sqrt(3)/2) * leg).

Now, we can solve for the height:

Height = (sqrt(3)/2) * leg = (sqrt(3)/2) * base * ((sqrt(3)/2) * leg).

Simplifying further, we have: Height = (3/4) * leg.

Therefore, the height of the triangle is (3/4) times the length of the leg.

ЗАРАНЕЕ ОГРОМНОЕ СПАСИБО!!!!)))