Solving Triangles with the Law of Cosines

Jun 30, 2025

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Learn about the Law of Cosines used to solve non-right triangles. Explore how it complements the Law of Sines for triangle trigonometry problems. Discover how to apply the Law of Cosines effectively.

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Solving Triangles with the Law of Cosines

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Section 5.7
The Law of Cosines
The Law of Cosines Like the Law of Sines, we use this to solve triangles that are not right triangles (no 90° angles). The Law of Cosines can help to solve triangles that the Law of Sines can not solve.
Law of Cosines (cont.) These all represent the same law, just different ways of showing it…
Example Solve ΔABC if A = 52°, b = 6 and c = 8.
Example #2 Solve ΔABC if a = 21, b = 16.7 and c = 10.3.

5.7

5.7. Find Angle Measure in Polygons. 2. 3. 1. 4. 5. 6. Theorem 5.16: Polygon Interior Angles Theorem. The sum of the measures of the interior angles of a convex n -gon is ( n – __ ) . _____. Corollary to Theorem 5.16: Interior Angles of a Quadrilateral.

389 views • 12 slides

Section 5.7- Proving that Figures are Special Quadrilaterals.

Section 5.7- Proving that Figures are Special Quadrilaterals. By, Michael Thiel and Lauren Larar . . What Family?. First, you must identify what family the quadrilateral falls under. Parallelogram , Trapezoid , quadrilateral. Proving that a quadrilateral is a Rectangle.

333 views • 18 slides

Section 5.7 Numerical Integration

Section 5.7 Numerical Integration. a. b. a. b. a. b. Approximations for integrals: Riemann Sums, Trapezoidal Rule, Simpson's Rule Riemann Sum: Trapezoidal Rule: Simpson’s Rule: Approximation by Approximation by Approximation by

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Notes 5.7

Imaginary/Complex Numbers Complex Conjugates. Notes 5.7. Notes 5.7 Given the fact i 2 = ________ The imaginary number is _____ w hich equals _____. Complex numbers are written in the form: _______________ Where “a” is a real number and bi is an imaginary number.

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Section 5.7 Financial Models

Section 5.7 Financial Models. A credit union pays interest of 4% per annum compounded quarterly on a certain savings plan. If $2000 is deposited in such a plan and the interest is left to accumulate, how much is in the account after 1 year?.

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Section 5.7

Section 5.7. Systems of Inequalities And Linear Programming. Linear Inequality in Two Variables. An inequality that can be written as Ax + By < C or Ax + By > C , where A, B, and C are real numbers and A and B are not both 0. The symbol < may be replaced with , >, or .

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Exercise 5.7

Exercise 5.7. MICROECONOMICS Principles and Analysis Frank Cowell. March 2007. Ex 5.7: Question. purpose : Illustration of labour supply model with very simple preferences method : Consumer optimisation with endogenous budget constraint. Ex 5.7: Worker’s problem.

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Section 5.5 (and 5.7)

Section 5.5 (and 5.7). Integration by Substitution & Natural Logs. The Chain Rule & Integration. How do we handle something like this? Think back to how we took the derivative of a composite function like. -Substitution. Example 1.

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Lesson 5.7

Lesson 5.7. Systems of Inequalities. You have learned that a solution to a system of two linear equations, if there is exactly one solution is the coordinates of the point where the two lines intersect. In this lesson you will learn about systems of inequalities and their solutions.

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Section 5.7

Chapter 5. Section 5.7. Exercise #1. Find each. the first term the common difference the twelfth term the sum of the first 12 terms. 5 , 13 , 21 , 29 , 37 …. a). the first term. b). the common difference. 5. = 8. 13  5. 5 , 13 , 21 , 29 , 37 …. c).

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Section 5.7 Hot Issues

Section 5.7 Hot Issues. A: Genesis: review of the “marsupial paradigm” See: http://www.atmos-chem-phys-dicuss.net/9/19159/2009/acpd-9-19159-2009.html The following slides were made available by Tim Dunkerton B: Genesis: role of Kelvin waves Guest Lecturer Michael Ventrice – April 28 th.

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Section 5.7 Arithmetic and Geometric Sequences

Section 5.7 Arithmetic and Geometric Sequences. What You Will Learn About. Arithmetic Sequences Geometric Sequences. Sequences. A sequence is a list of numbers that are related to each other by a rule. The terms in a sequence are the numbers that form the sequence. Arithmetic Sequence.

3.6k views • 18 slides

5.7

5.7. Analyzing graphs of Quadratic Functions. Most basic quadratic function is y = x 2 Axis of Symmetry is x = 0 Vertex is (0, 0) A family of graphs is a group of graphs that displays one or more similar characteristics! y = x 2 is called a parent graph.

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Section 5.7

Section 5.7 Suppose X 1 , X 2 , …, X n is a random sample from a Bernoulli distribution with success probability p . Then Y = X 1 + X 2 + … + X n has a distribution. According to the Central Limit Theorem, can be treated as having an approximate N (0, 1)

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Section 5.7 Solving recurrence relations

Section 5.7 Solving recurrence relations. One typical problem of this type is to find an explicit formula for the n -th term ( a n ) of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, … where the recurrence relation is a n = a n -1 + a n -2.

478 views • 18 slides

Section 5.7- Proving that Figures are Special Quadrilaterals.

Section 5.7- Proving that Figures are Special Quadrilaterals. By, Michael Thiel and Lauren Larar. What Family?. First, you must identify what family the quadrilateral falls under. Parallelogram , Trapezoid , quadrilateral. Proving that a quadrilateral is a Rectangle.

419 views • 18 slides

Section 5.7 Arithmetic and Geometric Sequences

Section 5.7 Arithmetic and Geometric Sequences. What You Will Learn. Arithmetic Sequences Geometric Sequences. Sequences. A sequence is a list of numbers that are related to each other by a rule. The terms are the numbers that form the sequence. Arithmetic Sequence.

242 views • 19 slides

5.7

5.7. Arithmetic and Geometric Sequences. Objectives Write terms of an arithmetic sequence. Use the formula for the general term of an arithmetic sequence. Write terms of a geometric sequence. Use the formula for the general term of a geometric sequence. Sequences.

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Section 5.7

Section 5.7. Compound Interest. The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is. COMPOUND INTEREST.

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SECTION 5.7

SECTION 5.7. HYPERBOLIC FUNCTIONS. INVERSE FUNCTIONS. Certain combinations of the exponential functions e x and e – x arise so frequently in mathematics and its applications that they deserve to be given special names.

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Section 5.7: Additional Techniques of Integration

Section 5.7: Additional Techniques of Integration. Practice HW from Stewart Textbook (not to hand in) p. 404 # 1-5 odd, 9-27 odd. Integrals Involving Powers of Sine and Cosine. Two Types

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