Question

Угол BAE=112° Угол ДB=68° BC=9 см Найдите AC

Answer 1

Дано:

∠BAE = 112°

∠DBF = 68°

BC = 9 см

Найти:

AC - ?

Решение:

1) ∠BAC и ∠BAE - смежные ⇒ ∠BAC = 180° - ∠BAE = 180° - 112° = 68°

2) ∠DBF и ∠ABC - вертикальные ⇒ ∠ABC = ∠DBF = 68°

3) ΔACB - равнобедренный, т.к. углы при основании равны ⇒ AC = BC = 9 см

Answer 2

To find the length of AC, we can use the Law of Cosines since we have two sides and the included angle in triangle ABC.

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where: c = length of the side opposite to angle C (AC in this case) a = length of one side and the included angle (BC in this case) b = length of the other side and the included angle (AB in this case) C = angle between sides a and b (angle BAE in this case)

Let's calculate AC:

Given: Angle BAE = 112° (C) Angle DB = 68° BC = 9 cm (a)

We need to find AC (c).

Step 1: Calculate the length of AB (b).

Since ABC is a triangle, the sum of its angles is 180°. Angle ABC = 180° - Angle BAE - Angle DB Angle ABC = 180° - 112° - 68° Angle ABC = 180° - 180° Angle ABC = 0°

An angle of 0° in a triangle means that the points A, B, and C are collinear (lie on the same straight line). Therefore, AB is part of the line segment BC, and the length of AB is equal to the length of BC.

So, AB = BC = 9 cm (b).

Step 2: Now we can calculate AC using the Law of Cosines.

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(C) AC^2 = 9^2 + 9^2 - 2 * 9 * 9 * cos(112°)

Now, calculate cos(112°) using a calculator (or computer software): cos(112°) ≈ -0.30901699437

AC^2 = 81 + 81 - 2 * 9 * 9 * (-0.30901699437) AC^2 = 162 + 49.54508555203 AC^2 = 211.54508555203

Step 3: Find the square root of AC^2 to get AC.

AC ≈ √211.54508555203 AC ≈ 14.548 cm

Therefore, the length of AC is approximately 14.548 centimeters.