Question

Помогите решить с рисунком треугольник abc угол c равен 90. биссектриса bd угла b равна 20 см, cd равна 10 см. найти da

Answer 1

DA = 10 см. Так как CD=DA

Answer 2

Triangle Calculation

To solve for the length of side DA in triangle ABC, where angle C is 90 degrees, the length of the bisector BD of angle B is 20 cm, and the length of CD is 10 cm, we can use the following steps:

1. Use the Angle Bisector Theorem: - The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides of the triangle.

2. Apply the Angle Bisector Theorem to Find the Length of AB and AC: - Using the Angle Bisector Theorem, we can find the lengths of AB and AC.

3. Apply the Pythagorean Theorem: - Once we have the lengths of AB and AC, we can apply the Pythagorean Theorem to find the length of side DA.

Solution Steps

1. Using the Angle Bisector Theorem: - The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides of the triangle.

2. Applying the Angle Bisector Theorem to Find the Length of AB and AC: - Let's denote the length of AB as x and the length of AC as y. - According to the Angle Bisector Theorem: - BD/DC = AB/AC - 20/10 = x/y - 2 = x/y - x = 2y

3. Applying the Pythagorean Theorem: - Using the Pythagorean Theorem, we can express the relationship between the sides of a right-angled triangle: - a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the other two sides.

4. Finding the Length of DA: - We know that AC = 2y and AB = y. Given that angle C is 90 degrees, we can use the Pythagorean Theorem to find the length of side DA: - DA^2 = AC^2 + AB^2 - DA^2 = (2y)^2 + y^2 - DA^2 = 4y^2 + y^2 - DA^2 = 5y^2 - DA = y√5

Conclusion

The length of side DA in triangle ABC is y√5.