Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
?
Intros
Lessons
0/4
?
Examples
Lessons
  1. Given the following triangle ABC\triangle ABC,
    Using law of sines to find angles and side lengths of triangles
    1. Solve forC\angle C
    2. Solve for aa
  2. Solve for side xx
    law of sines and side lengths of triangles
    1. Ambiguous case: SSA triangles
      In DEF\triangle DEF, DE=21cmDE=21cm, \angle F=45F=45°, and EF=24cmEF=24cm; find DFDF.
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
      • Easily See Your Progress

        We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
      • Make Use of Our Learning Aids

        Last Viewed
        Practice Accuracy
        Suggested Tasks

        Get quick access to the topic you're currently learning.

        See how well your practice sessions are going over time.

        Stay on track with our daily recommendations.

      • Earn Achievements as You Learn

        Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
      • Create and Customize Your Avatar

        Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
      Topic Notes
      ?
      In this section, we will learn about the Law of Sines, also known as the Sines Rule. The Law of Sines is a formula that models the relationship between the sides and the angles of any triangle, be it a right-angled triangle, an obtuse triangle, or an acute triangle. In order to use the Law of Sines, we need to satisfy the "one pair, one additional information" condition (i.e. Angle-Angle-Side abbreviated as AAS, and Angle-Side-Angle abbreviated as ASA). We will also explore the concept of the Ambiguous Case of the Law of Sines.
      Law of Sine
      For any \triangle ABC,

      asin(A)\frac{a}{\sin(A)} =bsin(B)=\frac{b}{\sin(B)} =csin(C)=\frac{c}{\sin(C)}
      and,
      sin(A)a\frac{\sin(A)}{a} =sin(B)b=\frac{\sin(B)}{b} =sin(C)c=\frac{\sin(C)}{c}

      Use the Law of Sine when given a pair!

      Ambiguous case
      Ambiguous case of the Law of Sine arises when given SSA (side-side-angle)

      Step 1) Use the given angle to find the height of the triangle: h=bsin(A)h=b \sin (A)

      Step 2) Check if,
      Side  aSide\;a < hh,
      then no triangles
      Side  a=hSide\;a=h,
      then 1 triangle
      Side  aSide\;a > hh,
      then 1 triangle
      hh < Side  aSide\;a < Side  bSide\;b,
      then 2 triangles

      Step 3) Solve the triangle(s)!