Question

identifying triangle sides
name:
find the length of the side listed.

1. find the length of side c.

a
/ \\
/ \\
c-----b
123.6 102.6 123.4

1. find the length of side c.

a
/ \\
/ \\
c-----b
153.3 100 162.2

1. find the length of side a.

a
/ \\
/ \\
c-----b
133 100.5 157.9

1. find the length of side b.

a
/ \\
/ \\
c-----b
112.3 101.3 109.9

1. find the length of side a.

c
/ \\
/ \\
b-----a
99.5 111.8 101

1. find the length of side a.

c
/ \\
/ \\
b-----a
156.9 148.4 100.7

Explanation:

Problem 1: Find the length of side C.

Step1: Recall triangle side - length identification (assuming it's a triangle with given two sides, maybe using triangle inequality or direct reading? Wait, maybe it's a typo and actually, these are triangles where we can sum or use some property? Wait, no, looking at the numbers, maybe it's a triangle where we have to check if it's a triangle (sum of two sides > third side) but actually, maybe it's a typo and the triangles are labeled with sides, so maybe side C is between the other two? Wait, no, let's check the first triangle: A has length 123.6, B has length 102.6, and the side from C to B is 123.4. Wait, maybe it's a triangle with vertices A, B, C, and we need to find the length of side C (which is the side opposite? No, side C is the side connecting C to... Wait, maybe the labels are: side A is between B and C, side B is between A and C, side C is between A and B? Wait, no, in triangle notation, side a is opposite angle A, side b opposite angle B, side c opposite angle C. But here, the problem says "Find the length of side C", so maybe side C is the side between A and B? Wait, no, looking at the first triangle: A is a vertex, B is a vertex, C is a vertex. The side from A to B is... Wait, the numbers: 123.6 (A to C), 102.6 (A to B), 123.4 (B to C). Wait, that can't be a triangle because 102.6 + 123.4 = 226 > 123.6, 123.6 + 102.6 = 226.2 > 123.4, 123.6 + 123.4 = 247 > 102.6. So it is a triangle. But the problem is to find the length of side C. Wait, maybe side C is the side opposite angle C, which is side AB? Wait, no, side AB would be between A and B. Wait, the length of side AB: in the first triangle, A to B: if A to C is 123.6, B to C is 123.4, and A to B is 102.6? No, that doesn't make sense. Wait, maybe it's a typo and the triangles are labeled with sides: side A is length 123.6, side B is length 102.6, and we need to find side C (length 123.4)? No, that's already given. Wait, maybe the problem is to check which side is which, but no, the problem says "Find the length of the side listed". Wait, maybe it's a mistake and the sides are labeled as: for the first triangle, side C is the side with length... Wait, no, the first triangle has: from C to A: 123.6, from C to B: 123.4, from A to B: 102.6. So side C (the side between A and B) would be 102.6? No, that's side AB. Wait, I think there's a mislabeling. Wait, maybe the sides are labeled as: side A is BC, side B is AC, side C is AB. So side C is AB. So in the first triangle, side C (AB) has length 102.6? But that's given. Wait, this is confusing. Wait, maybe the problem is to find the length of the side that is labeled C, i.e., the side connecting C to... Wait, the first triangle: vertices C, A, B. The side from C to A is 123.6, from C to B is 123.4, from A to B is 102.6. So if we need to find the length of side C, maybe side C is the side between A and B? But that's 102.6? No, that can't be. Wait, maybe it's a mistake and the problem is to find the length of the side that is not labeled, but no. Wait, maybe it's a triangle where we have to use the Law of Cosines? Let's try Law of Cosines. For triangle with sides a, b, c, c² = a² + b² - 2ab cos(C). But we don't have angles. Wait, maybe the triangles are isoceles or something. Wait, first triangle: 123.6, 123.4, 102.6. These are close to each other. Wait, maybe it's a typo and the length of side C is 102.6? No, that's side AB. Wait, I think I'm misunderstanding the labeling. Let's assume that in each triangle, the sides are labeled as follows: side A is the side opposite vertex A (between B and C), side B is opposite vertex B…

Step1: Identify the sides of the second triangle.

Vertices: A, B, C.
Side AC: 153.3, Side BC: 162.2, Side AB: 100.

Step2: Determine the length of side C.

Assuming side C is the side between A and B (AB), its length is 100.

Step1: Identify the sides of the third triangle.

Vertices: A, B, C.
Side AC: 133, Side BC: 157.9, Side AB: 100.5.

Step2: Determine the length of side A.

Assuming side A is the side between B and C (BC), its length is 157.9? No, wait, side A is opposite angle A, so side a is BC. But the problem says "Find the length of side A". If side A is the side between B and C, then length is 157.9. But wait, AC is 133, AB is 100.5, BC is 157.9. So side A (BC) is 157.9? No, maybe side A is the side between A and C (AC), which is 133. Wait, the problem says "Find the length of side A". Let's assume side A is the side opposite angle A, which is BC, length 157.9. But that's given. Alternatively, side A is the side between A and B, which is 100.5. No, this is confusing. Wait, maybe the labeling is: side A is the side with label A, i.e., the side from A to C is 133, so side A is 133. So the length of side A is 133.

Answer:

102.6

Problem 2: Find the length of side C.