Question

The area of a triangle is 2. Two of the side lengths are 2.1 and 3.8 and the includedangle is acute. Find the measure of the included angle, to the nearest tenth of adegree.

Answer 1

`C=30.1\degree`

Step-by-step explanation

The area of a triangle using two given sides and the included angle is given as:

`A=(1)/(2)a\cdot b\cdot\sin C`

where a and b are the sides and C is the included angle.

Therefore, we have to find C given that:

`\begin{gathered} A=2 \\ a=2.1 \\ b=3.8 \end{gathered}`

Therefore, we have that:

`\begin{gathered} 2=(1)/(2)\cdot2.1\cdot3.8\cdot\sin C \\ \Rightarrow\sin C=(2\cdot2)/(2.1\cdot3.8)=0.5012 \\ \Rightarrow C=\sin ^(-1)(0.5013) \\ C=30.1\degree \end{gathered}`

That is the measure of the included angle.