Question

find the perimeter of each triangle. Round to the nearest tenth. m<C =109 , a=9cm and b=5cm

Answer 1

find the perimeter of each triangle. Round to the nearest tenth. m<=109, a=9cm and b=5cm

Solution

The perimeter of triangle

$$P = a + b + c.$$

According to the Law of cosines we can find the third side of a triangle using two sides and the angle between them:

$$\begin{array}{l} c = \sqrt {a ^ {2} + b ^ {2} - 2 a * b * \cos C} = \sqrt {9 ^ {2} + 5 ^ {2} - 2 * 9 * 5 * \cos 109} \\ c = \sqrt {81 + 25 - 2 * 9 * 5 * (-0.325568)} = 11.6 \text{ cm}. \end{array}$$

So let's find the perimeter of triangle

$$P = 9 + 5 + 11.6 = 25.6 \text{ cm}.$$

Answer: 25.6 cm.