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Trigonometry: Law of Sines

The Law of Sines can be thought of as an extension of basic right triangle trig ratios. In each of the problems below the Law of Sines can be used to reach a solution to the problem. However, several of the problems, such as Adventure Airlines, can also be solved by just using right triangle trigonometry.

More information about the Law of Sines can be found in the Ask Dr. Math archives. A derivation of the Law of Sines and an explanation of solving triangles using the Law of Sines are examples of what you can find when exploring the High School Trigonometry area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Trigonometry in our Internet Mathematics Library.


Access to these problems requires a Membership.

Additional Signals - Lisa Lavelle
Trig/Calc, difficulty level 2. Help locate Joey's and Erin's new friend. ... more>>

Adventure Airlines - Leigh Nataro
Trig/Calc, difficulty level 1. How far from the airport does the plane need to begin its descent? ... more>>

Coordinateville - Leigh Nataro
Trig/Calc, difficulty level 1. Find the angle of intersection of two roads based on given information. ... more>>

Goose Bay Mountain - Johnson, Patnode, Desautels, Brault, Mahoney
Trig/Calc, difficulty level 2. Using trigonometry, find the angle of takeoff needed for a plane to clear a mountain. ... more>>

How Do You Measure a Mountain? - Leigh Nataro
Trig/Calc, difficulty level 2. Find the height of a mountain based on two angles and the height of a nearby hill. ... more>>

How Large Is The Yard? - Leigh Nataro
Trig/Calc, difficulty level 2. Given three sides and two included angles, find the area of my parents' quadrilateral-shaped backyard. ... more>>

Kite Construction - Leigh Nataro
Trig/Calc, difficulty level 2. Given some information about the dimensions of a kite, find its area. ... more>>

Skiing in Vermont - Leigh Nataro
Trig/Calc, difficulty level 2. How far must you ski and what does your heading need to be for you to return to your starting point? ... more>>

Stonybrooke River Bridge - Leigh Nataro
Trig/Calc, difficulty level 2. Based on given information, find the distance across a river. ... more>>

The Supermarket Shelf - Leigh Nataro
Trig/Calc, difficulty level 3. What is the optimal shelf height in the supermarket? ... more>>

Triangles, Sines, and Areas - Leigh Nataro
Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A). ... more>>

Up, Up, and Away (Part II) - Leigh Nataro
Trig/Calc, difficulty level 3. Find the compass setting required to send a balloon on the shortest route from Honolulu, Hawaii, to Essex Junction, Vermont. ... more>>

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