Question

Дан треугольник ABC.Угол А=82, а=15, в=11. Найдите углы В, С, с.

Answer 1

Решим задачу, используя теорему синусов:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

$sinB= \frac{sinA*b}{a} =\frac{sin82*11}{15} =0,726$

∠B = 46,57°
∠C = 180° - 82° - 46,57° = 51,43°

$c= \frac{sinC*a}{sinA} = \frac{sin51,43*15}{sin82}= 11,85$

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Answer 2

Given Information:

Угол А = 82 a = 15 b = 11

To find angles B, C, and side c, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.

Step 1: Finding Angle B

We can use the Law of Sines to find angle B. 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. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Using the given information, we can set up the equation:

15/sin(82) = 11/sin(B)

To solve for angle B, we can rearrange the equation:

sin(B) = (11 * sin(82)) / 15

Now, we can find the value of angle B by taking the inverse sine (also known as arcsine) of both sides of the equation:

B = arcsin((11 * sin(82)) / 15)

Using a calculator, we can find that B ≈ 49.02 degrees.

Step 2: Finding Angle C

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

C = 180 - A - B C = 180 - 82 - 49.02 C ≈ 48.98 degrees

So, angle C is approximately 48.98 degrees.

Step 3: Finding Side c

Now that we have found angles B and C, we can use the Law of Sines again to find side c. We can use the same equation as before:

15/sin(82) = c/sin(C)

To solve for side c, we can rearrange the equation:

c = (15 * sin(C)) / sin(82)

Using a calculator, we can find that c ≈ 9.95 units.

Therefore, the angles of the triangle ABC are: A = 82 degrees B ≈ 49.02 degrees C ≈ 48.98 degrees

And the length of side c is approximately 9.95 units.