Question

Solve triangle ABC using the given measurements if $A=10{}^{\circ },C=90{}^{\circ }\text{and}b=15$. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short answer

The solution for triangle ABC,is $a=2.5,c=15.2\text{and}B=80°$.

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 $A=10{}^{\circ },C=90{}^{\circ }\text{and}b=15$.

Step 2. Calculation.

In triangle ABC, $A=10{}^{\circ },C=90{}^{\circ }\text{and}b=15$. Therefore, $B=80°$ by angle sum property.

Now, in right triangle ABC by trigonometric ratios,

$\begin{array}{c}\sin B=\frac{b}{c}\\ \sin \left(80°\right)=\frac{15}{c}\\ c=15\csc \left(80°\right)\\ c=15.2\end{array}$

Now, in right angle triangle ABC by Pythagoras Theorem,

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {\left(15.2\right)}^2=a^2+{\left(15\right)}^2\\ a^2={\left(15.2\right)}^2-{\left(15\right)}^2\\ a=\sqrt{{\left(15.2\right)}^2-{\left(15\right)}^2}\\ a=2.5\end{array}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=2.5,c=15.2\text{and}B=80°$.