Question

Угол треугольника ABC такие что А : B : C = 2 :3 :5 Чему равны углы треугольника​

Answer 1

Ответ:

a:b:c = 2:3:5 = 2x:3x:5x

Сумма углов треугольника равна 180°

2х+3х+5х+=180

10х=180°

х=18°

Найдем градусную меру углов треугольника

2х=36

3х=54

5х=90

Углы треугольника равны следовательно 36°,54°,90°

Answer 2

To find the angles of the triangle ABC when given the ratio of the sides, we need to use the fact that the angles of any triangle add up to 180 degrees. We'll first find the measures of the angles corresponding to the sides in the given ratio and then scale them to satisfy the total sum of 180 degrees.

Let's assume the measures of the angles are A, B, and C, corresponding to the sides in the ratio 2:3:5.

Step 1: Find the measures of the angles corresponding to the sides in the given ratio. Given: A : B : C = 2 : 3 : 5

Let the common ratio be k. So, A = 2k, B = 3k, and C = 5k.

Step 2: Use the fact that the sum of the angles of a triangle is 180 degrees. A + B + C = 180

Now, substitute the expressions for A, B, and C in terms of k: 2k + 3k + 5k = 180

Step 3: Solve for k. 10k = 180 k = 18

Step 4: Find the values of A, B, and C using k. A = 2k = 2 * 18 = 36 degrees B = 3k = 3 * 18 = 54 degrees C = 5k = 5 * 18 = 90 degrees

So, the angles of triangle ABC are: Angle A = 36 degrees Angle B = 54 degrees Angle C = 90 degrees