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.

Short answer

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

Step-by-step solution

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.

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