Question

The unknown triangle ABC has angle A = 20° and sides a ABC? 3 and c = 4. How many solutions are there for triangle Select the correct answer below:

a. 0 triangles
b. 1 triangle
b. 2 triangles
c. Infinitely many triangles

Answer 1

There is only one triangle that satisfies the given conditions.

Step-by-step explanation:

To determine the number of solutions for triangle ABC, we can use the Law of Sines and the given information. The Law of Sines states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively, the ratio of the sine of an angle to the length of its opposite side is constant. In this case, we have side a = 3 and side c = 4, and angle A = 20°. We can set up the equation sin(A)/a = sin(C)/c and substitute the known values. This gives us sin(20°)/3 = sin(C)/4. Solving for sin(C), we find sin(C) = (4/3)sin(20°).

We can use the inverse sine function to find the measure of angle C. By taking the inverse sine of (4/3)sin(20°), we get C ≈ 49.3°. Now, we can find angle B by subtracting the sum of angles A and C from 180°. B = 180° - 20° - 49.3° = 110.7°.

Therefore, there is only one triangle that satisfies the given conditions.