Question

In triangle ABC, a = 4, b = 6, and cos C = − 1/4. What is the length of side c?

(1)8
(2)2√7
(3)2√10
(4)4

Answer 1

The length of side c would be 8.

Explanation:

Given that,

a = 4

b = 6

cosC = -1/4

If we are given two sides and angle, the law of Cosines can be used to find the third side:

`c^(2) = a^(2) + b^(2) - 2ab (cos(c))`

By inserting the values in the formula, we get

`c^(2) = 4^(2) + 6^(2) - 2.4.6 (-(1)/(4) )`

`c^(2) = 16 + 36 + 12`

`c^(2) = 64`

`\sqrt{c^(2) } = √(64)`

c = 8.

Therefore, the length of side c would be 8.