Solve the triangle. round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 11, b = 109° a. b = 14.1, a = 24°, c = 47° b. b = 19.9, a = 22°, c = 49° c. b = 17, a = 26°, c = 45° d. no triangle

Option A is correct.

Step-by-step explanation:

Given: a = 6 , c = 11 ,  B = 109°

To find : b , ∠A , ∠C

We use Law of cosine and Law of sines.

Law of Cosine used for calculating one side of a triangle when the angle opposite and the other two sides are known.

b² = a² + c² - 2ac.cos B

Law of Sines is a rule relating the sides and angles of any triangle.

Using Law of Cosines, we get

b² = 6² + 11² - 2 × 6 × 11 × cos 109

b² = 199.97

b = 14.1 (nearest tenth)

Now using Law of sines, we get

∠ A = 23.8° = 24° (nearest degree)

Using Angle sum property of triangle,

∠A + ∠B + ∠C = 180°

∠C = 180 - (24 + 109)

∠C = 47°

Therefore, Option A is correct.

other answer is correct. i had used the radius of the radius somehow. a website:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .