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Law of Cosines Teacher Resources
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In this Law of Cosines worksheet, 10th graders solve 10 different problems related to applying the Laws of Cosine. First, they determine the length of a side rounded to the nearest integer. Then, students determine the largest angle of a triangle described to the nearest degree. In addition, they determine the length of a larger diagonal of a rhombus.
This worksheet provides excellent practice in applying the Law of Sines and the Law of Cosines. It consists of six problems, each of which presents a real-world scenario with an accompanying diagram. The task in each exercise is to answer a specific question about the scenario. To answer the question, learners must use the appropriate law and interpret the result within the context of the problem. You could use these exercises in several different ways. Set up stations around the classroom with an exercise at each station, use them for independent practice or homework, have students work in groups to complete them, or use them for assessment.
Need a quick calculation for the area of an ellipse, or the volume of the triangular pyramid? There are 39 different solvers in this app, to give you the answer to numerous geometry and trigonometry problems.
If solving trigonometric equations is your idea of fun, then this video is correctly titled. Here Sal uses trigonometric identities, the quadratic formula, and inverse trigonometric functions to solve a trigonometric equation sent in by a listener. Maybe a member from your class could send in the next featured problem.
Sal solves an interesting question in this video from a college entrance exam in India that requires one to use knowledge of arithmetic progressions, trigonometric identities, and algebra. He works through solving the problem in a step-by-step fashion by talking through his thought process in order to help one follow the solution as well as understand why certain steps are taken.
In this video, Sal solves another navigation problem that combines the SOH-CAH-TOA model and the relationship between distance, rate, and time. The most challenging part of this problem is probably the set up, and he does a good job of drawing out exactly what problem needs to be solved.
In an involved problem from the American Invitational Mathematics Exam from 2004, Sal logically shows the multi-step solution. He uses geometric properties of hexagons, parallelograms, and triangles, trigonometric identities, and the Pythagorean Theorem to arrive at the solution.
The next time you are at an amusement park you may want to consider all the interesting math problems you could do! Using trigonometric ratios, some logic and algebra, Sal solves a problem in this video of finding a personï¿½s height off the ground at any given time while riding a Ferris wheel. This might also be an interesting problem for learners to graph to see how the function is sinusoidal and how the problem can be adjusted to change the amplitude and period of the graph.
Sal solves a question from a college entrance exam in India which asks one to find the maximum value of a rational expression with trigonometry ratios. To solve this problem, Sal finds a maximum value by finding the minimum value of the denominator. He uses trigonometric identities to simplify the expression and then finds where the derivative of the denominator is zero and answers the questions whether or not it is a minimum or maximum value. This is an interesting problem that mixes trigonometry and calculus skills.
Students take an Algebra II/Trigonometry sample test. For this Algebra II/Trigonometry sample sample test lesson, students take a sample test for Algebra 2/Trigonometry. Students solve 39 multiple choice/short answer questions about topics including radicals, equations of circles, exponential equations, angle measures, etc.
In this solar storms worksheet, students use a diagram given the location of two STEREO spacecraft satellites, a coronal mass ejection, the sun and the Earth to solve 2 problems about the coronal mass ejection. Students use segments, angles and trigonometric identities to determine the length of a segment in the diagram. They determine the length the coronal mass ejection traveled and the time it took to travel that length.
Investigate non-linear functions based upon the characteristics of the function or the representation of the function. The functions are displayed in multiple formats including as graphs, symbols, words, and tables. Learners use written reflection scored on a rubric to assess understanding.