Question

Solve the right trianglea=1.9 in, A=46.5°, C=90°Round to one decimal placeDraw the right triangle

Answer 1

ANSWER and EXPLANATION

We want to solve the triangle with the given measurements.

Let the triangle be triangle ABC

First, we can find the third angle in the triangle. The sum of angles in a triangle is 180 degrees. This implies that:

`46.5+B+90=180`

Solve for B:

`\begin{gathered} B+_{}136.5=180 \\ B=180-136.5 \\ B=43.5\degree \end{gathered}`

Now, we can find the lengths of the sides by using the sine rule:

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

where b and c are the sides opposite angles B and C respectively.

Therefore, we have that:

`(\sin46.5)/(1.9)=(\sin43.5)/(b)=(\sin 90)/(c)`

From the first two equations:

`\begin{gathered} b=(1.9\cdot\sin 43.5)/(\sin 46.5) \\ \Rightarrow b=1.8in \end{gathered}`

From the first and third equations:

`\begin{gathered} (\sin46.5)/(1.9)=(\sin 90)/(c) \\ \Rightarrow c=(1.9\cdot\sin 90)/(\sin 46.5) \\ c=2.6in \end{gathered}`

The solutions to the triangle are:

`\begin{gathered} b=1.8in \\ c=2.6in \\ B=43.5\degree \end{gathered}`

The diagram of the triangle is: