Chapter 8.6, Problem 36PPS

To determine

To calculate:

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

Answer to Problem 36PPS

The measurements of triangle are $m\angle W\approx {23}^{\circ },WS\approx 101.8,TW\approx 66.9$ .

Explanation of Solution

Given information:

  

Concept used:

Law of sines:

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

Calculation:

  

The sum of the angles of a triangle is $180$ . So,

  $m\angle W=180-\left(33+124\right)=23$

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 $TW$ .

Law of sines:

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

First substitute,

  $\frac{\sin 33}{WT}=\frac{\sin 23}{48}$

Cross products property,

  $WT\cdot \sin 23=48\cdot \sin 33$

Now, divide each side by $\sin 33$

  $WT=\frac{48\cdot \sin 33}{\sin 23}$

Now, get the value of $WT$ ,

  $WT\approx 66.9$

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

Substitute,

  $\frac{\sin 124}{WS}=\frac{\sin 23}{48}$

Cross products property,

  $WS\cdot \sin 23=48\cdot \sin 124$

Now, divide each side by $\sin 23$

  $WS=\frac{48\cdot \sin 124}{\sin 23}$

Now, get the value of $WS$ ,

  $WS\approx 101.8$

Therefore, the measurements of triangle are $m\angle W\approx {23}^{\circ },WS\approx 101.8,TW\approx 66.9$