Law of sines: Sinca) = sin(B) = sin(C)
How many distinct triangles can be formed for which mA
= 75°, a = 2, and b = 3?
No triangles can be formed.
One triangle can be formed where angle B is about 15°.
One triangle can be formed where angle B is about 40°
Two triangles can be formed where angle B is 40° or
140°

no trangles can be formed

Step-by-step explanation:

We have been given angle A as 75 degrees and sides a = 2 and b = 3.

Using Sine rule, we can set up:

sin(a)                    sin(b)

     =      

A                              B

Upon substituting the given values of angle A, and sides a and b, we get:

sin(75)                   sin(B)

     =      

2                                3

Upon solving this equation for B, we get:

>3sin(75)=2sin(B)

>sin(B)=3sin(75)

                      2

>sinB=1.4488

Since we know that value of Sine cannot be more than 1. Hence there are no values possible for B.

Hence, the triangle is not possible. Therefore, first choice is correct.

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pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.