Chapter 14.3, Problem 22PPSE

Solution

To find: the remaining sides and angles of the given triangle.

  $A={52.6}^{\circ },B={37.4}^{\circ },c\approx 10.2$ .

Given:

  $a=8.1,b=6.2$ .

Concept used:

The sum of two acute angles of a right triangle is complementary.

Pythagorean Theorem: In any right triangle, the sum of squares of the lengths of two legs is equal to the

Square of the hypotenuse.

Calculation:

Let us draw the right triangle by using the given values as follows:

  

In the above triangle,

  $\begin{array}{c}\tan B=\frac{6.2}{8.1}\\ B={37.43}^{\circ }\\ B\approx {37.4}^{\circ }\end{array}$

Now since the sum of two acute angles of a right triangle is complementary, therefore

  $\begin{array}{c}A+B={90}^{\circ }\\ A+{37.4}^{\circ }={90}^{\circ }\\ A={52.6}^{\circ }\end{array}$

Now by using the Pythagorean Theorem in the triangle ABC, it follows that

  $\begin{array}{c}{\left(8.1\right)}^2+{\left(6.2\right)}^2=c^2\\ 65.61+38.44=c^2\\ c^2=104.05\\ c=\sqrt{104.05}\\ c=10.2004\\ c\approx 10.2\end{array}$