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Problem 1 :.

## Ambiguous Case - Law of Sines Worksheet

A researcher wants to determine the width of a pond from east to west, which cannot be done by actual measurement. From a point P, he finds the distance to the eastern-most point of the pond to be 8 km, while the distance to the western most point from P to be 6 km.

Solution :. Problem 2 :.

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Here we use the formula for cos C, because we know the length of b and c. Problem 3 :. A straight tunnel is to be made through a mountain. Given that :.

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Multiplication tricks. Test - I.One side of the proportion has side A and the sine of its opposite angle. The other side of the proportion has side B and the sine of its opposite angle. When you know 2 sides and the non-included angle or when you know 2 angles and the non-included side. There are two different situations when you use this formula.

But really, there is just one case. Just look at it: You can always immediately look at a triangle and tell whether or not you can use the Law of Sines -- you need 3 measurements: either 2 sides and the non-included angle or 2 angles and the non-included side.

The picture below illustrates a case not suited for the law of sines. Since we do not know an opposite side and anglewe cannot employ the formula. Or, just look at it : Remember when you have 2 sides, the angle must be non -included.

In which triangle s below, can we use the formula? Both triangles below have 3 known measurements. Triangle 1 has only one opposite pair that we are dealing with, but that does not help us because we need to know both the angle and its opposite side.

Triangle 2 does have 2 opposite pairs that we are dealing with, and we do know the measurements of one angle and its opposite side. Or, just look at it : We can use the formula, when we have 2 sides and the non -included angle. In the full practice problems below, we will solve for triangle 2's unknown angle measure. We can not use side with length 20 because we don't know its opposite angle. And, of course, we do not know the measure of the angle opposite of the side of length 13 because Just look at it: Remember when you have 2 sides, the angle must be non -included. Or just look at it: Remember when you have 2 angles, the side must be non -included. Follow up from question 3. Now, use the formula for law of sines to determine the measure of the labelled side to the nearest tenth. Question taken from our law of sines downloadable pdf worksheeet. Is it possible to use the law of sines to calculate x pictured in the triangle below?

Yes, first you must remember that the sum of the interior angles of a triangle is in order to calculate the measure of the angle opposite of the side of length What is the length of side CB?

The easiest one is to use sohcahtoa to solve for a side length to arrive at the answer. Law of Sines worksheet 25 question worksheet with answer key.

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Law of Sines vs Cosines When to use each one. For instance, let's look at Diagram 1. Diagram 1. Case I. Triangle 2 does have 2 opposite pairs that we are dealing with, and we do know the measurements of one angle and its opposite side Or, just look at it : We can use the formula, when we have 2 sides and the non -included angle.

Show Answer. Step 2 Solve for unknown. Can we use the law of sines to solve for the labelled angle? No, because we need to know the measure of 1 opposite side and angle.

Question taken from our law of sines downloadable pdf worksheeet Show Answer.General Questions To approximate the length of a lake, a surveyor starts at one end of the lake and walks yards. Approximately how long is the lake? Two ships leave port at 4 p. One is headed at a bearing of N 38 E and is traveling at The other is traveling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p. You are heading to Beech Mountain for a ski trip.

Unfortunately, state road in North Carolina is blocked off due to a chemical spill. You have to get to Tynecastle Highway which leads to the resort at which you are staying. NC would get you to Tynecastle Hwy in After 6 miles, there is another turn that leads to Tynecastle Hwy. Assuming that both roads on the detour are straight, how many extra miles are you traveling to reach your destination? The distance on a map from the airport in Miami, FL to the one in Nassau, Bahamas is kilometers due east. Bangor, Maine is northeast of both cities; its airport is kilometers from Miami and kilometers from Nassau.

What bearing would a plane need to take to fly from Nassau to Bangor? To keep it from falling, we nailed a 6-foot strap into the ground 4 feet from the base of the tree. How far from vertical was the tree leaning? Site Navigation. Word Problem Exercises: Law of Cosines. General Questions. To approximate the length of a lake, a surveyor starts at one end of the lake and walks yards.

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Students will solve problems using the law of sines or law of cosines. Some of the problems ha. MathPreCalculusTrigonometry. OtherActivitiesFun Stuff. Add to cart. Wish List.

Word Problems - Law of Sines and Cosines. For example, word problem card, diagram card, equation card, calculator-ready equation card, and final answer card. This activity can be used in numerous ways. However, I used it to introduc. GeometryTrigonometryWord Problems. ActivitiesCooperative Learning.

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This packet contains formulas, notes, examples, and a question practice test with solutions ; and, bonus 7 question test. NOTE: The free preview file is identical to th. MathTrigonometry.Word math problems Worksheets Calculators. The Law of Sines - math word problems The aspect ratio The aspect ratio of the rectangular triangle is 5.

### Law Of Sines And Cosines Word Problems Worksheet Kuta

Calculate the internal angles of the triangle. Use the law of sines. Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long.

Determine the size of the inner trapezoid angles. What is the height of the pole? The observer's distance from P is m. Determine the viewing angle of P and observer. Calculate the length of the shortest side, write the result in cm up to two decimal places. Water channel The cross section of the water channel is a trapezoid. The width of the bottom is Calculate how much water flows through the channel in 5 minutes if the water flo Diamond diagonals Calculate the diamond's diagonal lengths if its content is cm 2 and the side length is 13 cm.

Two triangles SSA Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. What is the length of side AC? Angles and sides of the triangle Triangle ABC has a circumference of 26 cm. Arrange the interior angles in order of its size.

From one end of the fence is m. How far is it from the another end of the fence? Calculate width of the river.

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## Law Of Sines And Cosines Word Problems Worksheet Kuta

Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox. Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etcFarmer Chuck Norris needs to enclose a triangular field along a river.

One side of fencing is already in place, and Farmer Chuck has 40 feet of fence for the open side. How far away from point A along the river can Farmer Chuck put the fence? Joey must find the distance from Point A to Point B on opposite sides of a lake. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B. Played 83 times. Print Share Edit Delete.

Live Game Live. Finish Editing. This quiz is incomplete! To play this quiz, please finish editing it. Delete Quiz. Question 1. Law of Sines. Law of Cosines. Which Law would you use? What is the measure of angle A? Jack is flying his kite. He runs feet away from his house and lets out 75 feet of string.

The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house? Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle.In any given triangle, the ratio of the length of a side and the sine of the angle opposite that side is a constant.

The Law of Sines is also known as the sine rule, sine law, or sine formula. It is valid for all types of triangles: right, acute or obtuse triangles. We can use the Law of Sines when solving triangles. Solving a triangle means to find the unknown lengths and angles of the triangle. We will first consider the situation when we are given 2 angles and one side of a triangle. We will now consider the situation when we are given two sides and an obtuse angle of a triangle.

The only valid value for Q is We will now consider the situation when we are given two sides and one angle of a triangle. If you are given two sides and a non-included acute angle and the side facing the given angle is less than the other side, you would obtain two sets of answers. The solution is said to be ambiguous.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Lessons with examples, solutions, and videos to help High School students learn to use the law of sines.

### Law of Sines and Cosines Worksheet PDF

In these lessons, we will learn the Law of Sines how to use the Law of Sines when given two angles and one side how to use the Law of Sines when given two sides and a non-included angle about the ambiguous case when using the Law of Sines about the "no solutions" case when using the Law of Sines the proof for the Law of Sines how to solve applications or word problems using the Law of Sines Law of Sines The Law of Sines states that In any given triangle, the ratio of the length of a side and the sine of the angle opposite that side is a constant.

The following figure shows the Law of Sines for the triangle ABC The law of sines states that We can also write the law of sines or sine rule as: The Law of Sines is also known as the sine rule, sine law, or sine formula. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.