Chapter 8.6, Problem 35PPS

To determine

To calculate:

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

Answer to Problem 35PPS

The measurements of triangle are $m\angle G\approx {75}^{\circ },m\angle J\approx {71}^{\circ },HJ\approx 20.3$ .

Explanation of Solution

Given information:

  

Concept used:

Law of sines:

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

Calculation:

  

With the help of the above diagram it is easy to get the two sides and a nonincluded angle. So, with the help of the Law of sines get the measure of angle $J$ .

Law of sines:

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

First substitute,

  $\frac{\sin J}{20}=\frac{\sin 34}{11.8}$

Cross products property,

  $\sin J\cdot 11.8=\sin 34\cdot 20$

Now, solve for $J$

  $\sin J=\frac{\sin 34\cdot 20}{11.8}$

Now, get the value of $J$ ,

Use the inverse sine ratio

  $J\approx 71$

Now, the sum of angles of triangles is $180$ . So,

  $m\angle G=180-\left(34+71\right)=75$

Since, as know the two sides and a nonincluded angle, use the law of sines to get $HJ$ .

Substitute,

  $\frac{\sin 75}{HJ}=\frac{\sin 34}{11.8}$

Cross products property,

  $HJ\cdot \sin 34=\sin 75\cdot 11.8$

Now, solve for $HJ$

  $HJ=\frac{\sin 75\cdot 11.8}{\sin 34}$

Now, get the value of $HJ$ ,

  $HJ\approx 20.3$

Therefore, the measurements of triangle are $m\angle G\approx {75}^{\circ },m\angle J\approx {71}^{\circ },HJ\approx 20.3$