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Law of Sines - Printable Mathematics Worksheets - Wayground

Law of Sines

10 questions

11th - 11th Grade

Mathematics

Law of Sines is a Grade 11 mathematics worksheet that builds procedural fluency with solving oblique triangles, including the ambiguous case. Students work through 10 questions: five multiple-choice items and five fill-in-the-blank calculations. The questions ask them to choose the correct first step, set up Law of Sines proportions, enter an inverse-sine calculation, identify a potential second angle solution, and determine unknown angle or side measures to the nearest tenth or hundredth. This free printable worksheet with an answer key helps students connect the setup, calculator work, and numerical solution steps required for non-right-triangle problems. It is useful for guided practice after introducing the Law of Sines, independent review, or a quick check of whether students can recognize when a second solution may exist. The final self-reflection item also gives students a structured way to report their confidence with the ambiguous case and identify whether they need more practice.

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Worksheets

Law of Sines

Total questions: 10

Name
Class
Date
1.

If you were told to solve the triangle given: <B=27°, a=28 b=18<B=27\degree,\ a=28\ b=18  

What would be your first step.

a)

find side c using pythagorean theorem

b)

Set up a proportion to find angle C

c)

Set up a proportion to find angle B

d)

Set up a proportion to find angle A

2.

If you were told to solve the triangle given: <B=27°, a=28 b=18<B=27\degree,\ a=28\ b=18  

What would you type in the calculator to find <A?

a)

sin⁡A=28sin⁡2718\sin A=\frac{28\sin27}{18}  

b)

sin⁡−1(28sin⁡2718)\sin^{-1}\left(\frac{28\sin27}{18}\right)  

c)

sin⁡(28sin⁡2718)\sin\left(\frac{28\sin27}{18}\right)  

d)

sin⁡−1(18sin⁡2728)\sin^{-1}\left(\frac{18\sin27}{28}\right)  

3.

How do you find the potential second solution for <A?

a)

∠A1−90°\angle A_1-90\degree   

b)

hope you can see someone's paper to steal their answer 

c)

180−∠A1=∠A2180-\angle A_1=\angle A_2   

d)

use a law of sine proportion 

4.

What is ∠A2=\angle A_2=  

to the nearest tenth?

(a)  

5.

What is the measure of ∠C1=\angle C_1=  

to the nearest tenth?

(a)  

6.

What is the measure of ∠C2=\angle C_2=   

to the nearest tenth?

(a)  

7.

What proportion should you set up to find c1=c_1=  

a)

18sin⁡108.1=csin⁡27\frac{18}{\sin108.1}=\frac{c}{\sin27}  

b)

18sin⁡27=c108.1\frac{18}{\sin27}=\frac{c}{108.1}  

c)

1827=c108.1\frac{18}{27}=\frac{c}{108.1}  

d)

18sin⁡27=csin⁡108.1\frac{18}{\sin27}=\frac{c}{\sin108.1}  

8.

What is c1=c_1=  ?

(a)  

9.

What is c2=c_2=  ?

(a)  

10.

How do I feel about ambiguous case?

a)

I want to cry! But with more practice I will cry less :)

b)

I feel better now but I need more practice.

c)

Still iffy :/ but I know that with extra practice I'll be good to go.

d)

I am an expert but I will welcome the opportunity for extra practice.

Answer Key

Law of Sines

Total questions: 10

1.
d)

Set up a proportion to find angle A

2.
b)

sin⁡−1(28sin⁡2718)\sin^{-1}\left(\frac{28\sin27}{18}\right)  

3.
c)

180−∠A1=∠A2180-\angle A_1=\angle A_2   

4.
135.1
5.
108.1
6.
17.9
7.
d)

18sin⁡27=csin⁡108.1\frac{18}{\sin27}=\frac{c}{\sin108.1}  

8.
37.69
9.
12.19
10.
n/a

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FAQs

What does this Law of Sines worksheet help students learn?

This Grade 11 worksheet helps students solve oblique triangles by selecting the correct Law of Sines proportion, entering an inverse-sine calculation, and checking for a possible second angle in the ambiguous case. Its five multiple-choice questions target setup and reasoning, while five fill-in-the-blank items require students to calculate unknown measures and round their answers appropriately.

How can I use this worksheet to teach the Law of Sines and the ambiguous case?

Use the multiple-choice items first as a guided sequence: have students explain why they choose a particular proportion, demonstrate the calculator entry for the first angle, and discuss how the potential second angle is found. Then assign the five numerical fill-in items so students apply the process independently, followed by a review of the final confidence check to identify which step needs reteaching.

What mistakes should I watch for on this Law of Sines worksheet?

Watch for students choosing the wrong known angle-side pair when setting up a proportion, entering the ratio incorrectly in the calculator, or rounding before completing the calculation. In the ambiguous-case items, students may find only the first angle and overlook the potential second solution; the fill-in questions also reveal whether they can carry the correct angle or side measure through to the requested precision.

How do I assign and grade this Law of Sines worksheet?

You can assign this Law of Sines worksheet as a printable PDF or as a digital quiz on Wayground, and it includes a complete answer key for the five multiple-choice and five fill-in-the-blank questions. For printable submissions, scan student work with the Wayground for Teachers app to help grade responses efficiently.

How can I differentiate this Law of Sines worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the proportions, calculator-entry prompts, and fill-in calculations are easier to follow. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those worksheet-level formats support your learners.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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