Question

СРОЧНО ПОМОГИТЕ ПАДАЛУЙСТА!!! 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 the ratio of the length of a side of a triangle 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 set up the following equation:

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.

Since the sum of the angles in a triangle is 180°, we can find angle A by subtracting angles B and C from 180°:

A = 180° - B - C

Substituting the given values, we have:

A = 180° - 60° - 45° = 75°

Now we can use the law of sines to find the length of side AC:

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

9 / sin(75°) = BC / sin(60°)

To find the value of sin(75°), we can use a calculator or reference table. The value of sin(75°) is approximately 0.9659.

Substituting the values, we have:

9 / 0.9659 = BC / sin(60°)

Simplifying the equation, we get:

9.321 = BC / 0.8660

To find the length of side BC, we can multiply both sides of the equation by 0.8660:

9.321 * 0.8660 = BC

BC ≈ 8.08 cm

Therefore, the length of side AC in triangle ABC is approximately 9 cm.

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

Using the law of sines, we can set up the following equation:

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.

Since the sum of the angles in a triangle is 180°, we can find angle C by subtracting angles A and B from 180°:

C = 180° - A - B

Substituting the given values, we have:

C = 180° - 45° - 105° = 30°

Now we can use the law of sines to find the length of side AC:

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

AC / sin(45°) = 16 / sin(105°)

To find the value of sin(105°), we can use a calculator or reference table. The value of sin(105°) is approximately 0.9659.

Substituting the values, we have:

AC / 0.7071 = 16 / 0.9659

Simplifying the equation, we get:

AC ≈ 11.31 cm

Therefore, the length of side AC in triangle ABC is approximately 11.31 cm.

Please note that the values provided are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.