Q9. - Algebra 2

Question

Solve triangle ABC using the given measurements if $A=45{}^{\circ },C=90{}^{\circ }\text{ and } b=6$. Round measure of sides to the nearest tenth and angles to nearest degree.

Step-by-Step Solution

Answer

The solution for triangle ABC, is $a=6,c=8.5\text{ and }B=45°$.

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $A=45{}^{\circ },C=90{}^{\circ }\text{ and } b=6$. 

Step 2. Calculation.

In triangle ABC, $A=45{}^{\circ },C=90{}^{\circ }\text{ and } b=6$. Therefore, $B=45°$ by angle sum property.

Now  $\begin{array}{c}\angle A=\angle B\text{ gives,}\mathrm{....}\left(45°\text{\hspace{0.33em}each}\right)\\ a=b\\ a=6\end{array}$

Now, in isosceles right triangle ABC,

 $\begin{array}{c}c=\sqrt{a^2+b^2}\text{\hspace{0.17em}gives,}\\ c=\sqrt{6^2+6^2}\\ c=6\sqrt{2}\\ c=8.5\end{array}$

Step 3. Conclusion.

The solution for triangle ABC, is $a=6,c=8.5\text{ and }B=45°$.