Question

1. # State Whether The Given Measurements Determine Zero, One, Or Two Triangles. C = 30°, A = 28, C = 14

## Introduction

Math has always been a difficult subject for many people. That’s because it forces us to look at the world in a way that we may not be used to. And when it comes to mathematics, there are a few things that are simply impossible to ignore. One of these is geometry—specifically, triangle measurements. In this blog post, we will explore the concept of zero, one, and two triangles and see if they can be determined using given measurements. Be prepared to be surprised!

## Zero Triangle

Zero triangle is a geometric figure that has zero length, width, and height. It can be created when two equal non-parallel lines are intersected at a right angle. In order to determine whether the given measurements determine zero, one, or two triangles, we must first figure out the lengths of each side.

If the length of one side is greater than the length of the other side, then the triangle will have an undefined shape and will not be able to be determined using the given measurements. If the length of one side is less than the length of the other side, then a triangle will be formed and both sides will be equal in length.

If the lengths of both sides are equal then we can use these measurements to determine whether a triangle exists or not. The shortest distance between any two points on a line is called a hypotenuse and it measures 120°. If you want to create a right angled triangle then you would need two 45° angles and one hypotenuse which would measure 175°. Therefore, if both measurements (120° + 175°) add up to 360° then there will be a right triangle present and all three angles would equal 180 degrees.

## One Triangle

The given measurements Determine zero, one, or two triangles. C = °, A = , C = .

C = °: If the given measurement is in degrees Celsius, then the triangle will be determined to be zero-length, one-length, or two-length.

A = : If the given measurement is in inches, then the triangle will be determined to be zero-width, one-width, or two-width.

## Two Triangles

Solving for zero, one, or two triangles is a common problem in geometry. In this blog post, we will discuss two triangles and how their measurements determine their outcome.

The first triangle has base angles of 60° and 120°. The second triangle also has base angles of 60° and 120°, but its height is double the length of the first triangle’s height.

When solving for zero, one, or two triangles, it is important to keep in mind the Pythagorean theorem. This theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. So in our first triangle, since C = °, A = , C = 360° – 120° + 90° = 270°. Therefore, C = 270° which determines that zero exists in this triangle.

Similarly, in our second triangle with base angles of 60° and 120° and height twice as long as the first triangle’s height (180°), A = 2×360° – 120° + 90° = 720°. Therefore: A = 720° which determines that one exists in this triangle.

## Conclusion

The measurements given determine that there are zero triangles, one triangle, and two triangles.

2. When analyzing if two measurements make up one, two, or zero triangles, it is important to understand the basics of triangle geometry. In order for a shape to be considered a triangle, three sides must be present and all three sides must possess an angle that can add up to 180 degrees. With this in mind, given the measurements C  30 , A  28 and C 14, one can determine whether zero, one or two triangles have been created.

The first step in determining if any triangles have been made is to analyze the angles presented by these three measurements. Using basic trigonometry we can see that when C  30 , A  28 and C 14 are applied together they form only one unique angle of 118 degrees – well short of the 180 degree requirement needed for a triangle. Therefore based on these figures alone no triangle has been formed using just those three sides listed.

3. 😕 Trying to determine if the given measurements can create zero, one, or two triangles can be a tricky task. Let’s take a closer look!

The measurements given are C = 30°, A = 28, C = 14. These measurements alone cannot determine the number of triangles possible. This is because the measurements refer to three sides and an angle of a triangle. We need to know at least one additional measurement in order to determine the number of triangles possible.

It is important to remember the three rules of triangles:

1. The sum of the three angles must always equal 180° .
2. A side length must always be greater than the difference between the other two side lengths.
3. No side length can be greater than the sum of the other two side lengths.

Given the measurements C = 30°, A = 28, and C = 14, we can use the 3 rules of triangles to determine the number of triangles possible.

First, let’s look at the angle measurement. C = 30°, which means that the other two angles must add up to 150°. We can use this to determine if one or two triangles are possible.

If one triangle is possible, then the other two angles must both be equal or the sum of the side lengths must be greater than the difference between the other two side lengths. However, if two triangles are possible, then the other two angles must be unequal and the sum of the side lengths must be less than the difference between the other two side lengths.

Given the measurements C = 30°, A = 28, and C = 14, we can determine that one triangle is possible. This is because the other two angles must be equal and the sum of the side lengths is greater than the difference between the other two side lengths.

Therefore, the given measurements determine one triangle 🤔.