State Whether The Given Measurements Determine Zero, One, Or Two Triangles. B = 84°, B = 28, C = 25

Introduction

Geometry is an essential part of the math curriculum and can be applied to everyday life. Understanding how to calculate measurements correctly and figure out how many triangles can exist based on those measurements leads to greater proficiency in mathematics. This blog post will look at one particular example: what happens when you have three given measurements that determine whether you have zero, one, or two triangles? In this case, we will look at the given measurements of B = 84°, B = 28, and C = 25. We will explain the importance of these three measurements and the steps to take in order to figure out the answer.

Zero Triangles

When it comes to geometry, a triangle is defined as a three-sided polygon. In order to determine whether the given measurements determine zero, one, or two triangles, we must first understand the properties of a triangle. A triangle must have three sides, and each side must be less than the sum of the other two sides. Additionally, the angle between each side must be less than 180 degrees. With that said, let’s take a look at the given measurements.

Based on the given measurements, it is safe to say that there are zero triangles. This is because the angle B is greater than 180 degrees, which goes against one of the properties of a triangle. If even one property of a triangle is not met, then it cannot be classified as a triangle. Therefore, in this case, zero triangles are determined by the given measurements.

One Triangle

It is given that B = °, B = , and C = . We must determine whether the given measurements determine zero, one, or two triangles.

Since we are given the measure of one angle and the lengths of two sides, we can use the Law of Cosines to find the measure of the third angle. We do this by finding the value of cosC.

We know that cosC = (a^2 + b^2 – c^2)/(2ab). We also know that a = 1, b = 1, and c = 2. Thus, cosC = (1^2 + 1^2 – 2^2)/(2*1*1) = 0.5.

This means that C = 60°. Since we now have the measures of all three angles, we can determine that the given measurements do in fact determine one triangle.

Two Triangles

If two angles and a side between them are given, then it is possible to determine whether zero, one, or two triangles can be formed. If the given measurements do not form a triangle, then it is not possible to solve for the other missing sides or angles.

To recall, a triangle is defined as a three-sided polygon. The sum of the interior angles of any triangle is 180°. To be classified as a unique triangle, no two sides can be equal and all three angles must be less than 180°. In addition, the longest side must be shorter than the sum of the other two sides.

With these criteria in mind, we can analyze the given measurements to see if they form zero, one, or two triangles. In this case, we are given that angle B equals 60° and angle C equals 60°. We are also told that side BC equals 3. Based on this information, it is not possible to form any triangles because two angles that sum to 60° cannot create an angle that sums to 180° with another side. Therefore, in this scenario, we would say that the given measurements determine zero triangles.

Conclusion

In conclusion, the given measurements of B = 84°, B = 28 and C = 25 determine two triangles. This is because the sum of all three measurements add up to 137 degrees which exceeds 180 degrees – the maximum amount required for a triangle to be formed. Therefore, this set of measurements result in two triangles being formed.