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:
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]
[tex]sinB =\frac{b\times sinA}{a}[/tex]
[tex]sinB =\frac{9\times sin(36^\circ)}{3}[/tex]
[tex]sinB =3\times 0.587[/tex]
[tex]sinB =1.74[/tex] (impossible)
There is no value of B so that [tex]sinB = 1.74 > 1[/tex]
Therefore, Zero triangle as we cannot construct a triangle with A = 36°, a = 3, b = 9
