Question

State whether the given measurements determine zero, one, or two triangles. A = 36°, a = 3, b = 9

Answer 1

Answer:

Zero triangle as we cannot construct a triangle with A = 36°, a = 3, b = 9

Step-by-step explanation:

Given : Measurements  A = 36°, a = 3, b = 9

To find : Whether the given measurements determine zero, one, or two triangles.

Solution : Suppose there is a triangle with A = 36°, a = 3, b = 9.

Applying sine law:  

$\frac{a}{sinA} =\frac{b}{sinB}$

$sinB =\frac{b\times sinA}{a}$

$sinB =\frac{9\times sin(36^\circ)}{3}$

$sinB =3\times 0.587$

$sinB =1.74$ (impossible)  

There is no value of B so that $sinB = 1.74 > 1$

Therefore, Zero triangle as we cannot construct a triangle with A = 36°, a = 3, b = 9

Answer 2

The given measurements determines zero triangles. Source: https://answers.yahoo.com/question/index?qid=20080804154329AA1gdUS