Question

Find the unknown sides and angles of this triangle using the Law of Cosines. Round to the nearest hundredth.

Answer 1

c=10.35

<a=50.87°

<b=87.13°

Explanation:

as we know

law of cosine

`c = \sqrt{ {a}^(2) + {b}^(2) - 2ab. \cos(c) }`

`c = \sqrt{ {14}^(2) + {18}^(2) - 2.14.18 - \cos( {35}^(o) ) }`

`c = 10.35`

using the law of cosine

`cos(a) = \frac{ {b}^(2) + {c}^(2) - {a}^(2) }{2bc}`

`\cos(a) = \frac{ {18}^(2) + {10.35 }^(2) - {14}^(2) }{2.18.(10.35)}`

`a = {50.87}^(o)`

b=87.13°