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!

Get the most by viewing this topic in your current grade. Pick your course now.

  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.
      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)}
      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)!