Chapter 8.6, Problem 31PPS

To determine

To calculate:

The triangle and angle measures and side measures to the nearest tenth.

Answer to Problem 31PPS

The measurements of triangle are $m\angle B\approx {34}^{\circ },AB\approx 9.5,CA\approx 6.7$ .

Explanation of Solution

Given information:

  

Concept used:

Law of sines:

  $a=b\frac{\sin \alpha }{\sin \beta }$

Calculation:

  

The sum of angle of a triangle that is $180$ .

  $m\angle B=180-\left(94+52\right)=34$

Since, with the help of the diagram it is easy to get that it has two sides and a nonincluded angle, now set up a proportion using the law of sines to get $AB$

First substitute,

  $\frac{\sin 52}{AB}=\frac{\sin 94}{12}$

Use the cross-product property,

  $AB.\sin 94=12.\sin 52$

Now, divide each side by $\sin 94$

  $AB=\frac{12.\sin 52}{\sin 94}$

Now get the value of $x$ ,

  $x\approx 9.5$

Similarly, use the law of sines to get the $CA$

First substitute,

  $\frac{\sin 3A}{CA}=\frac{\sin 94}{12}$

Use the cross products property,

  $CA.\sin 94=12.\sin 34$

Divide each side by $\sin 94$

  $CA=\frac{12\sin 34}{\sin 94}$

Now get the value of $x$ ,

  $x\approx 6.7$

Therefore, the measurements are $m\angle B\approx {34}^{\circ },AB\approx 9.5,CA\approx 6.7$