Question

АВС угол С =90градусов ВС=12см cos B=4/5 Найти АВ

Answer 1

Ответ:

Объяснение:

cos B= ВC/AB=4/5=12/АВ

АВ=12×5=60

60÷4=15

АC²=AB²-ВC² за теоремою Піфагора

АС²=15²-12²=225-144=81

АС=корінь із 81=9 см

Answer 2

Problem Statement

You are given a right triangle ABC, where angle C is 90 degrees, side BC has a length of 12 cm, and cos(B) is equal to 4/5. You need to find the length of side AB.

Solution

To find the length of side AB, we can use the cosine rule, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

The cosine rule states that for any triangle ABC with sides a, b, and c, and angle A opposite side a, the following equation holds:

a^2 = b^2 + c^2 - 2bc * cos(A)

In our case, we know that angle C is 90 degrees, so angle A is angle B. We also know that side BC has a length of 12 cm, and cos(B) is equal to 4/5.

Let's substitute the known values into the cosine rule equation:

AB^2 = 12^2 + c^2 - 2 * 12 * c * (4/5)

Simplifying the equation:

AB^2 = 144 + c^2 - 24c * (4/5) AB^2 = 144 + c^2 - 96c/5

Since we don't know the value of side AB, we'll leave it as AB^2 for now.

To find the value of c, we can use the fact that cos(B) is equal to 4/5. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, side BC is the adjacent side and side AB is the hypotenuse.

cos(B) = BC/AB 4/5 = 12/AB

Cross-multiplying the equation:

4 * AB = 5 * 12 4AB = 60

Dividing both sides by 4:

AB = 60/4 AB = 15 cm

Therefore, the length of side AB is 15 cm.

Answer

The length of side AB in the right triangle ABC, where angle C is 90 degrees, side BC has a length of 12 cm, and cos(B) is equal to 4/5, is 15 cm.