Question

Помогите пожалуйста! АВС известно, что АВ = 10 см, ВС = 4 см, СА = 8 см. На стороне АС обозначено точку D такую, что AD = 6 см. Найдите отрезок ВД. Рисунок и дано есть, нужно решение. Заранее спасибо!

Answer 1

Найдем косинус угла A по теореме косинусов из ΔАВС:
ВС² = AB² + AC² - 2·AB·AC·cos∠A
16 = 100 + 64 - 2·10·8·cos∠A
160cos∠A = 148
cos ∠A =  148 / 160 =  37/40

Теперь из ΔABD по теореме косинусов найдем сторону BD:
BD² = AB² + AD² - 2·AB·AD·cos∠A
BD² = 100 + 36 - 2·10·6· 37/40 = 136 - 111 = 25
BD = 5 см

Answer 2

Problem Analysis

We are given a triangle ABC, where AB = 10 cm, BC = 4 cm, and CA = 8 cm. Point D is marked on side AC such that AD = 6 cm. We need to find the length of segment BD.

Solution

To find the length of segment BD, we can use the property of similar triangles. Let's analyze the given information and use it to find the length of BD.

From the given information, we have: AB = 10 cm BC = 4 cm CA = 8 cm AD = 6 cm

We can see that triangle ABC is a right-angled triangle, where angle B is the right angle. Let's label the angles of triangle ABC as follows: Angle A = α Angle B = 90° Angle C = β

Using the Pythagorean theorem, we can find the value of angle α: sin(α) = BC / AC sin(α) = 4 / 8 sin(α) = 0.5 α = arcsin(0.5) α ≈ 30°

Now, we can use the property of similar triangles to find the length of BD. Triangle ABD is similar to triangle ABC, so we can set up the following proportion: AB / BC = AD / BD

Substituting the given values, we have: 10 / 4 = 6 / BD

Simplifying the equation, we get: 10 * BD = 4 * 6 10 * BD = 24 BD = 24 / 10 BD = 2.4 cm

Therefore, the length of segment BD is approximately 2.4 cm.

Conclusion

The length of segment BD is approximately 2.4 cm.