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Determining Angles and Side Lengths in Triangles, Lecture notes of Analytical Geometry and Calculus

Solutions to various problems related to finding the angles and side lengths of triangles, using theorems and the triangle angle-sum theorem. It covers different triangles with given angles and side lengths, and explains the reasoning behind the determination of the smaller and larger angles and sides.

What you will learn

  • What is a linear pair in a triangle and how can it be used to determine the lengths of sides?
  • How does the Triangle Angle-Sum Theorem help in finding the lengths of sides in a triangle?
  • Given the angles and sides of a triangle, how can you determine the smaller and larger angles?

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Listtheanglesandsidesofeachtriangleinorderfromsmallesttolargest.
15.
SOLUTION:
Basedonthediagram,weseethat ByTheorem5.9,themeasureoftheangleoppositethelonger
sidehasagreatermeasurethantheangleoppositetheshorterside,therefore 
Angle:
Side:
18.
SOLUTION:
BytheTriangleAngle-SumTheorem,
Therefore,byTheorem5.10weknowthatthesideoppositethegreaterangleislongerthan
thesideoppositealesserangleand
Angle:
Side:
eSolutionsManual-PoweredbyCogneroPage1
5-3InequalitiesinOneTriangle
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List the angles and sides of each triangle in order from smallest to largest.

SOLUTION: Based on the diagram, we see that By Theorem 5.9, the measure of the angle opposite the longer side has a greater measure than the angle opposite the shorter side, therefore Angle: Side:

SOLUTION: By the Triangle Angle-Sum Theorem, Therefore, by Theorem 5.10 we know that the side opposite the greater angle is longer than the side opposite a lesser angle and Angle: Side:

List the angles and sides of each triangle in order from smallest to largest.

SOLUTION: Using the Triangle Angle-Sum Theorem, we can solve for x, as shown below.

degrees, degrees and the degrees.

Therefore,. By Theorem 5.10, we know that the lengths of sides across from larger angles are longer than those across from shorter angles so. Angle: P , Q , M Side: SENSE-MAKING Use the figure to determine the relationship between the measures of the given angles.

  1. BFD, BDF SOLUTION: The side opposite is , which is of length 12. The side opposite is , which is of length 15. Since by Theorem 5.9.
  2. DBF, BFD SOLUTION: The side opposite is , which is of length 5. The side opposite is , which is of length 12. Since by Theorem 5.9.