Chapter 8.2, Problem 34AYU

In Problems 25-36, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s).

$b=4$, $c=5$, $B={95}^{\circ }$

To determine

To find: The given information results in one triangle, two triangles, or no triangle at all.

Answer to Problem 34AYU

Solution:

The given information results in no triangle.

Explanation of Solution

Given:

$\text{b} = 4, \text{c} = 5$ and $\text{B} = {95}^{\circ }$

Formula used:

$\frac{\text{sin}\text{A}}{\text{a}} = \frac{\text{sin}\text{B}}{\text{b}} = \frac{\text{sin}\text{C}}{\text{c}}$

$\angle \text{A} + \angle \text{B} + \angle \text{C} = {180}^{\circ }$

Calculation:

Two sides and one angle are known, use the law of sines to find the angle $\text{C}$

$\frac{\text{sin}\text{B}}{\text{b}} = \frac{\text{sin}\text{C}}{\text{c}}$

$\frac{\text{sin}95°}{4} = \frac{\text{sin}\text{C}}{5}$

$\text{sin}\text{C} = \frac{5\text{sin}95°}{4} \approx 1.24$

$\text{sin}$ value is never greater than 1 so from the given values we can’t form a triangle.