Question

State whether the given measurements determine zero, one, or two triangles. A = 80°, a = 24, b = 50

Answer 1

we know that
applying the law of sines
a/sin A=b/sin B---------> a*sin B=b*sin A
A = 80°, a = 24, b = 50
sin B=[b*sin A]/a-----> sin B=50*sin 80/24-----> sin B=2.0517

the sines value can not be greater than 1
hence

the answer is
zero triangles

Answer 2

The zero triangle is formed because the value of sin B cannot be more than one.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a triangle.

The value of the sine function is [-1, 1]

A = 80°, a = 24, b = 50

We know that the sine rule

$\rm \dfrac{a}{sin\ A} = \dfrac{b}{sin\ B}\\\\\\sin\ B \ = \dfrac{b}{a} sin A$

Put all the value, we have

$\rm sin\ B \ = \dfrac{50}{24} sin 80^o\\\\sin \ B \ = 2.051$

The zero triangle is formed because the value of sin B cannot be more than one.

More about the trigonometry link is given below.

https://brainly.com/question/22698523