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

Answer:

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

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:

$\frac{a}{\sin A}=\frac{b}{\sin B}$

Substitute the given values:

$\begin{gathered} \frac{7}{\sin45}=\frac{6}{\sin B} \\ 7\times\sin B=6\times\sin 45 \\ \sin B=\frac{6\times\sin 45}{7} \\ B=\arcsin \mleft(\frac{6\times\sin45}{7}\mright) \\ B=37.3\degree \end{gathered}$

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.

$\begin{gathered} \frac{c}{\sin C}=\frac{b}{\sin B} \\ \frac{c}{\sin 97.7\degree}=\frac{6}{\sin 37.3} \\ c=\frac{6}{\sin37.3}\times\sin 97.7\degree \\ c=9.8m \end{gathered}$

Thus, the solution to the triangle is:

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