Question

Find the area of the triangle described below. Round to the nearest hundredth.C = 91°10'. a = 24, b = 5

Answer 1

We need to convert Angle C to only degrees.

Since

`\begin{gathered} 1^0=60^(\prime) \\ \Rightarrow x^{}=10^(\prime) \\ \\ \Rightarrow1^0*10^(\prime)=60^(\prime)* x \\ \\ \Rightarrow x=(10)/(60)=(1)/(6)^0 \end{gathered}`
`\Rightarrow C=91^010^(\prime)=(91+(1)/(6))^0=(547)/(6)^0`
`\begin{gathered} \text{ The area of a triangle A} \\ A=(1)/(2)a\cdot b\sin C \\ \\ \Rightarrow A=(1)/(2)\cdot24\cdot5\cdot\sin ((547)/(6))\approx59.99 \end{gathered}`