What is the value of x in the triangle?
15
30°
X
60°

x = 7.5

Step-by-step explanation:

Obviously, we can tell this is a right triangle, but to be more specific, it's a 30º-60º-90º triangle, meaning that one side is 90º, and the other two are 30 and 60 degrees.

When given a 30º-60º-90º triangle, you can solve the length of the other two sides even if only one side length is given. For a 30º-60º-90º triangle, the sides are given in x - x - 2x form. The side opposite the 30º is always x (which is given in the picture you provided), the side opposite the 60º is always x, and the side opposite the 90º is always 2x.

So the side opposite the 60º is 15, which is x. We can write an equation:

15 = x

÷  ÷

 = x

Now we can't leave a number with a square root at the bottom, so we multiply both the numerator and the denominator by .

= x

7.5 = x

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.