Question

Assume is opposite side a, is opposite side b, and is opposite side c. determine whether there is no triangle, one triangle, or two triangles. then solve each triangle, if possible. round each answer to the nearest tenth. (if not possible, enter impossible. below, enter your answers so that 1 is smaller than ₂.) a = 7, b = 3, = 24° ₁ = ° ₂ = ° ₁ = ° ₂ = ° c₁ = c₂ =

A. How many possible triangles can be formed with the given values of a, b, and ?
B. If a triangle is possible, calculate the values of ₁, ₂, ₁, and ₂.
C. If no triangle is possible, state "impossible."
D. What condition must be met for the given values to form a triangle?

Answer 1

To determine how many triangles can be formed with the given values of a, b, and ∠C, we can use the Law of Sines and the triangle inequality theorem.

Step-by-step explanation:

To determine how many triangles can be formed with the given values of a, b, and ∠C, we can use the Law of Sines which states that the ratio of the sine of an angle to the length of the opposite side is the same for all angles in a triangle.

First, we check for the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

If the triangle inequality theorem is satisfied, then we can determine the angles of the triangle using the Law of Sines. If not, it is impossible to form a triangle.