A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.

Question

Mathematics

Braedon Huff

12 December, 17:43

A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.

+2

Answers (1)

Know the Answer?

Thalia Weiss · Answer 1

Begin by using the cosine rule to find the unknown side.

Where a - unknown side, b is 12, c is 16 and angle in between is 108°

The cosine rule ...

a² = b² + c² - 2bc cosA

= 12² + 16² - (2*12*16 cos108°)

= 518.655076

Taking the positive square root ...

a = 22.774

a = 22.8 cm nearest tenth