Chapter 11.8, Problem 8AE

To determine

To determine the area of the given triangles.

Answer to Problem 8AE

Area of the given triangles are 18.4 and 28.54.

Explanation of Solution

Given information :

  

Here we shall use sine rule to determine the angles.

  

Here we know,

  $\begin{array}{l}\frac{6}{\sin {35}^{\circ }}=\frac{10}{\sin C}\\ \angle C={72.9}^{\circ },{107.1}^{\circ }\\ \angle A={72}^{\circ },{38}^{\circ }\end{array}$

When we solve the equation there are two possibilities of the triangles.

There two are the same as that shown in the question.

Now areas of the possible triangles are,

First possibility,

  $\frac{1}{2}ab\sin \theta =\frac{1}{2}\left(10\right)\left(6\right)\sin {72}^{\circ }=28.54$ .

Second possibility,

  $\frac{1}{2}ab\sin \theta =\frac{1}{2}\left(10\right)\left(6\right)\sin {38}^{\circ }=18.4$ .