Home > Math Topics > Trigonometry >

Application of the Standard Law of Sines

HSG-SRT.D.10
Answer Keys Here

Aligned To Common Core Standard:

High School Geometry - HSG-SRT.D.10

What is the Standard Law of Sines? Suppose that you have a triangle, and you have two known angles and one side as well. Now you think that you can figure the rest of the values of the triangle using the three values i.e. the remaining one angle and two sides. So, let's try figuring that out. One of the most common ways to do it is to use something that is called the Law of Sines. Let's see what those laws of sines are and how we can apply them. It is a fairly straightforward idea. The law of sines tells us that the ration between a Sine of an angle and the side opposite to it is going to be constant for any of the angles with the triangle. For example, if one angle is 30 and the other is 45, and altogether all sides need to be 180 degrees, then the remaining angle should be 105. Now you name the remaining two side as A and B. Now using the law of sine stated above, we can say that the sine of 30 divided by the length of the opposite (suppose it's 2) is going to be equal to sine of 105 divided by the length of A which is also going to be equal to sine of 45 divided by side b. We can choose any two sides at one time depending on what side we want to find first. So, after calculation, Sine 30/2 is equaled to 1/4 So, 1/4 = Sine 105/a, and 1/4 = Sine 45/b. Sine 45 = √2 / 2 | So, if we jump on to our calculations. We would find that the value of a is approximately is 3.86 and b is 2.83. Hence, this shows that when you have a few key values of a triangle, you can figure out the rest of the value using the law of sine. These worksheets and lessons will have students apply trig functions to help them find all types of unknown values of triangles.

Printable Worksheets And Lessons


  • Leg Length Step-by-Step Lesson- Find the leg of a triangle when you are given two angle measures and a side.
  • Guided Lesson - These problems all hover around the type of question you saw in the lesson.
  • Guided Lesson Explanation - The answers and process all start with the use of Sine equation.
  • Practice Worksheet - I focus most of the problems on finding legs of triangles because this is the most common question on the national exams.
  • Matching Worksheet - Match the lengths of legs to the missing parts of the triangles that are explained.


Homework Sheets

You are given some set dimensions and we ask you to find some missing sides and unknown lengths.

  • Homework 1 - In ∆ABC, side a =4, m< A = 40º and m< B = 30º. Find side b to the nearest tenth of an integer.
  • Homework 2 - Find the length of side x of the triangle.
  • Homework 3 - How do you arrange this to workout best.



Practice Worksheets

Some problems will give sides, some will give you angles, and others will give you both.

  • Practice 1 - Where does that value find itself?
  • Practice 2 - Why would you miss a single value in the tree?
  • Practice 3 - Find the length of g and don't forget about b.



Math Skill Quizzes

We work off of one basic triangle guide to answer these.

  • Quiz 1 - All questions use a differently sized variation of this labeled triangle.
  • Quiz 2 - Where is the missing side of that value.
  • Quiz 3 - Where are you going with this?