Free printable worksheet plus answer key on the ambiguous case of the law of sines includes visual aides, model problems, an online component and. Find the if shown in quadrant i is angle a with a sine of. After analyzing the ambiguous case for oblique triangles students will determine the number of possible solutions and find solutions when possible. In the video solving for an angle with the law of sines, sal solves for only one of the two possible solutions.
The law of sines can only be used when exactly one triangle can be built. One reallife application of the sine rule is the sine bar, which is used to measure the angle of a tilt in engineering. Ssa is known as the ambiguous case when using the law of sines because the given information may result in one triangle, two triangles, or no triangle at all. This law of sines law of cosines foldable flip book is designed for geometry, algebra 2, or precalculus depending upon curriculum. Using the law of sines to solve the ssa case the ambiguous case in the saa and asa cases objective 2, a unique triangle is always formed. Keep on lengthening side a until there are two possible triangles formed by the given info this is know as the ambiguous case. Beyond right angle trigonometry when we first started talking about. Lesson 3 ambiguous case of sine law ssa occurs when you are given ssa but the triangle is not constructed depending on the measure of the angle and the lengths of the sides, it may be possible to construct and therefore solve 0, 1, or 2 triangles. T he law of sines allows us to solve triangles that are not rightangled, and are called oblique triangles. How can the law of sines be used in problems involving the ambiguous case.
What links here related changes upload file special pages permanent link. We know that this triangle is a candidate for the ambiguous case since we are given two sides and an angle not in between them. Law of sines graphic organizer law of sines missing side missing angle ambiguous case steps ambiguous case no solution ambiguous case 2 solutions ambiguous case 1 solution b 102 c 43 b 21 a 42 a 22 b 12 1. Students will understand when the law of sines can be used to. With the following two math lib activities, students will practice using the law of sines and law of cosines to find missing side and angle measures in triangles. The sine function is positive in the first and second quadrant, but calculators are designed to display the first angle as a result. Use the law of sines to find measure of angle a in this scenario. The ambiguous case ssa if we are given two sides and an angle opposite one of the two sides ssa, the given information may result in one triangle, two triangles, or no triangle at all. Furthermore, as a result, you might have to analyze the situation before applying the law of sines and solving for the missing pieces. Proof of the law of sines this is a topic in traditional trigonometry. The ratio of the length of a side of a triangle to the sine of the angle opposite that. Understanding and solving the ambiguous case for the law of sines has never been easier with this sure fire method and 7 detailed. Because, ssa triangles can yield us one triangle, two triangles, or no triangles. We also discovered that ssa did not work to prove triangles.
Model problems in the following example you will find the possible measures of an angle given the sine of the angle. If it helps, you can draw a rough sketch to view this triangle, but this is optional. When using the law of sines to find a side of a triangle, an ambiguous case occurs when two separate triangles can be constructed from the data provided i. May 02, 2016 learn how to solve a triangle using the law of sines when it is the ambiguous ssa case in this free math video tutorial by marios math tutoring. The ambiguous case ssa occurs when we are given two sides and the. So, there are situations where the information were provided with for a triangle make it possible for. What quantities should you check before applying the law of sines. Find all solutions for triangle and round to nearest tenth. When using the law of sines to find a side of a triangle, an ambiguous case occurs when. Plan your 60minute lesson in math or law of sines with helpful tips from katharine sparks. Option 1 option 2 16 16 do both options make legal triangles.
Other common examples include measurement of distances in navigation and measurement of the distance between two stars in astronomy. Eleventh grade lesson ambiguous case day 1 of 2 betterlesson. This lesson covers the ambiguous case of the law of sines. In its default state, the side length a is clearly not long enough to form a real triangle. Included are two flip books with both guided examples and practice problems. Law of sines and law of cosines math lib bundle math lib activities are a class favorite. The sides of a triangle are to one another in the same ratio as the sines of their. A 40o a b c a b c 20 in 20 in 25 in 25 in 40o 40o 2 possible pictures if b 53. In the ssa case given two sides and the angle opposite one of the sides 3 possibilities exist.
Use the law of sines to find missing angles and sides of a nonright triangle. If you are given two sides and a nonincluded acute angle and the side facing the given angle is less than the other side, you would obtain two sets of answers. The law of sines can be used to solve for sides and angles of oblique triangles. One book includes the ambiguous case of the law of sines, and the other does not. The ssa caseone triangle solve abc with c 122, a 12 cm, and c 18 cm. This concept is often difficult for students to visualize because it involves turning one triangle into two when certain conditions are met. Sas side, angle, side asa angle, side, angle aas angle, angle, side sss side, side, side hl hypotenuse leg for right triangles. By downloading this file you are agreeing to the terms of use. Dec 22, 2016 ambiguous case law of sines in geometry, we found that we could prove two triangles congruent using. For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles ssa. Adjust the slider for a until it is just long enough to form one triangle.
Such triangles are called oblique or scalene triangles. Jan 21, 2020 ambiguous means that something is unclear or not exact or open to interpretation. There is another possible answer to this question and that is the coterminal angle of 106. So, if we encounter a triangle that has ssa congruency, we have an ambiguous triangle in the sense that we need to investigate more thoroughly.
Ill try to make it look a little strange so you realize it can apply to any triangle. Given two sides and an angle opposite one side ssa triangle. Ambiguous case of law of sines worksheet pdf with answer key. Given two sides and a nonincluded angle of a triangle, you might not be able to determine what type of triangle it is, or even if those pieces form a triangle at all. This situation is also known as the ambiguous case. The sides of a triangle are to one another in the same ratio as the sines of their opposite angles. In the case shown below they are triangles abc and ab. In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the.
For this project, i decided to demonstrate a trigonometric concept. The law of sines relates all angles and sides of a triangle in the following way, in which the lowercase letters indicate the side directly across from the capitalized angle. Teaching this particular topic in the past has created numerous headaches for both me and my students. Because c is obtuse and the side opposite c is longer than the given adjacent side, you know that only one triangle can be formed. Proof of the law of sines w e use the law of sines and the law of cosines to solve triangles that are not rightangled. We will now consider the situation when we are given two sides and one angle of a triangle ambiguous case.
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