Question

For ΔDEF, d=6, e=24, and m∠E=38°, How many triangles can be formed?

Answer 1

To determine the number of triangles that can be formed, use the Law of Sines, Angle Sum Property, and Triangle Inequality Theorem.

Step-by-step explanation:

To determine the number of triangles that can be formed, we need to consider the side lengths and angle measures of triangle DEF. Given that d = 6, e = 24, and m∠E = 38°:

1. We can use the Law of Sines to find the measure of angle D or angle F.
2. Once we have the measure of one of these angles, we can use the Angle Sum Property to find the measure of the third angle.
3. Finally, we can use the Triangle Inequality Theorem to determine if the given side lengths can form a triangle.

By following these steps, you can determine the number of triangles that can be formed.