Question

Find the missing side or angle.Round to the nearest tenth.C=95°b=6a=5c=[?]

Answer 1

c = 8.1

Explanation:

C = 95°

b = 6

a = 5

c = ?

Two sides, 1 angle, 1 unknown side

We will apply cosine rule:

$c^2=a^2+b^2\text{ - 2abcosC}$$\begin{gathered} c^2=5^2+6^2\text{ - 2(5)(6)}\times\text{cos95} \\ c^2\text{ = 25 + 36 - 60(cos 95)} \end{gathered}$$\begin{gathered} c^2\text{ = 61 - 60(-0.0872)} \\ c^2\text{ = 61 + 5.232} \\ c^2\text{ = 66.232} \end{gathered}$$\begin{gathered} square\text{ root both sides:} \\ c\text{ = }\sqrt[]{66.232} \\ c\text{ = 8.14} \\ \\ To\text{ the nearest tenth, c = 8.1} \end{gathered}$