You're given two side lengths of 10 centimeters and 8 centimeters. The angle between the sides measures 40°. How many triangles can you construct using these measurements? Answers = 0, 1, 2, infinitely many

Only one triangle can be constructed.

Step-by-step explanation:

We are given two side lengths of a triangle of 10 cm and 8 cm. The angle between the sides of the triangle measures 40°.

With the above-given data only one unique triangle can be constructed.

And the length of the third side can be calculated using the property of triangle as

a² = 10² + 8² - 2 * 10 * 8 Cos 40° {Where a is the length of the third side}

⇒ a² = 41.43

⇒ a = 6.44 cm. (Answer)