Question

В ABC треугольнике BC=5, A=30°, B=105° найдите AB-?

Answer 1

Ответ:

AB = 5√2

Пошаговое объяснение:

Дано :

ΔАВС

ВС = 5

∠А = α = 30°

∠В = 105°

Найти: АВ

Решение.

Сумма внутренних углов треугольника 180° и поэтому

β = ∠С = 180° - ∠А - ∠В = 180° - 30° - 105° = 45°

Применим теорему синусов

Ответ: AB = 5√2

Answer 2

To find the length of AB in the ABC triangle, we can use the law of sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant.

Let's use the law of sines to solve for AB:

sin(A) / BC = sin(B) / AB

First, let's find the value of sin(A) and sin(B):

sin(A) = sin(30°) = 0.5 sin(B) = sin(105°)

To find sin(105°), we need to use the sine addition formula:

sin(105°) = sin(60° + 45°) = sin(60°)cos(45°) + cos(60°)sin(45°) = (√3/2)(√2/2) + (1/2)(√2/2) = (√6 + √2) / 4

Now we can substitute the values into the law of sines equation:

0.5 / 5 = ((√6 + √2) / 4) / AB

To solve for AB, we can cross-multiply and solve the resulting equation:

0.5 * AB = 5 * ((√6 + √2) / 4)

AB = (5 * (√6 + √2)) / (4 * 0.5) = (5 * (√6 + √2)) / 2 = (5√6 + 5√2) / 2

Therefore, AB is equal to (5√6 + 5√2) / 2.