Question

Дано: AB + BC =12 ; угол CBA - 60° ; угол BCA - 90° Найти: AB ; BC

Answer 1

AB24
BC 180
Вот так вот

Answer 2

Given Information:

We are given the following information: - AB + BC = 12 - Angle CBA = 60° - Angle BCA = 90°

Solution:

To find the lengths of AB and BC, we can use trigonometric ratios in a right triangle.

Let's consider triangle ABC, where angle BCA is a right angle.

Using the trigonometric ratios, we can write:

sin(CBA) = AB / BC

cos(CBA) = BC / AB

Since we know that angle CBA is 60°, we can substitute the values:

sin(60°) = AB / BC

cos(60°) = BC / AB

Simplifying these equations, we get:

√3 / 2 = AB / BC

1 / 2 = BC / AB

We can solve these two equations simultaneously to find the values of AB and BC.

Multiplying the first equation by 2 and the second equation by √3, we get:

√3 = AB / BC

√3 = BC / AB

Equating the right sides of these equations, we get:

AB / BC = BC / AB

Cross-multiplying, we get:

AB^2 = BC^2

Taking the square root of both sides, we get:

AB = BC

Since we also know that AB + BC = 12, we can substitute AB with BC:

BC + BC = 12

Simplifying, we get:

2BC = 12

Dividing both sides by 2, we get:

BC = 6

Therefore, the length of BC is 6 units.

Since AB = BC, the length of AB is also 6 units.

Answer:

The length of AB is 6 units and the length of BC is 6 units.

Note: The search results did not provide any relevant snippets for this specific problem. However, the solution is derived using basic trigonometry principles in a right triangle.