Chapter 8, Problem 7RE

In Problems 6 and 7, solve each triangle.

To determine

To find: The value of $a, b$ and $A$

Answer to Problem 7RE

Solution:

$A \approx 66.4°, B \approx 23.6° and a = \surd 21$

Explanation of Solution

Given:

Formula used:

${\text{Opp}}^2 + {\text{adj}}^2 = {\text{hyp}}^2$

$\text{cos}\theta = \frac{\text{adjacent} \text{side}}{\text{hypotenuse}}$

$\text{sin}\theta = \frac{\text{opposite} \text{side}}{\text{hypotenuse}}$

Sum of the interior angles in a triangle is $180°$

Calculation:

${\text{Opp}}^2 + {\text{adj}}^2 = {\text{hyp}}^2$

From the figure,

$5² - 2² = a²$

$a = \surd 21$

$A + B = 90°$

$\text{Cos}A = \frac{2}{5}$

$A = {\cos }^{ - 1}\frac{2}{5} \approx 66.4°$

$\text{cos}B = \frac{2}{5}$

$B = {\cos }^{ - 1}\frac{\sqrt{21}}{5}$

$B \approx 23.6°$