Question

Determine the number of different triangles that he can form using the given measurements. Then solve the triangles. Round to the nearest tenth.pleasee help

Answer 1

`m\angle B=37.3\degree,m\angle C=97.7\degree,c=9.8m`

Step-by-step explanation:

Given:

`a=7m,b=6m,m\angle A=45\degree`

The given side is the longer of the two, so there will be only one solution.

Using Law of Sines:

`(a)/(\sin A)=(b)/(\sin B)`

Substitute the given values:

`\begin{gathered} (7)/(\sin45)=(6)/(\sin B) \\ 7*\sin B=6*\sin 45 \\ \sin B=(6*\sin 45)/(7) \\ B=\arcsin \mleft((6*\sin45)/(7)\mright) \\ B=37.3\degree \end{gathered}`

The sum of the angles in a triangle is 180 degrees.

`\begin{gathered} m\angle C=180-(\angle A+\angle B) \\ =180-(45+37.3) \\ =180-82.3 \\ m\angle C=97.7\degree \end{gathered}`

Finally, we find the length of c using the Sine rule.

`\begin{gathered} (c)/(\sin C)=(b)/(\sin B) \\ (c)/(\sin 97.7\degree)=(6)/(\sin 37.3) \\ c=(6)/(\sin37.3)*\sin 97.7\degree \\ c=9.8m \end{gathered}`

Thus, the solution to the triangle is:

`m\angle B=37.3\degree,m\angle C=97.7\degree,c=9.8m`