Question

ПОМОГОТЕ СРОЧНО! Найдите сторону АС трикутника АВС,если а)AC=9см B=60° C=45° в)BC=16 см A=45° B=105° Это синусы ​

Answer 1

Объяснение:

1) АС=9 см по условию

2) По теореме синусов АС=ВС*sin105:sin45=16*0,9659:0,7071=21,9 см.

Answer 2

Finding the Length of Side AC in Triangle ABC

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

Let's consider the given information for each case:

a) AC = 9 cm, angle B = 60°, angle C = 45°

Using the law of sines, we can write:

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

We are given AC = 9 cm, angle B = 60°, and angle C = 45°. We need to find angle A.

To find angle A, we can use the fact that the sum of the angles in a triangle is 180°:

A + B + C = 180°

Substituting the given values:

A + 60° + 45° = 180°

Simplifying the equation:

A + 105° = 180°

A = 180° - 105°

A = 75°

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

AC / sin(75°) = BC / sin(60°) = AB / sin(45°)

Substituting the given values:

9 / sin(75°) = BC / sin(60°) = AB / sin(45°)

Now we can solve for AC:

AC = 9 * sin(75°) / sin(45°)

Using a calculator, we find that:

AC ≈ 9.94 cm

b) BC = 16 cm, angle A = 45°, angle B = 105°

Using the law of sines, we can write:

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

We are given BC = 16 cm, angle A = 45°, and angle B = 105°. We need to find angle C.

To find angle C, we can use the fact that the sum of the angles in a triangle is 180°:

A + B + C = 180°

Substituting the given values:

45° + 105° + C = 180°

Simplifying the equation:

**150° + C