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Trigonometry: Law of Cosines

The Law of Cosines can be thought of as an extension of the Pythagorean theorem. In each of the problems below the Law of Cosines can be used as one of several steps needed to reach a solution. In the problems Up, Up and Away (Part I and Part II) the Law of Cosines is modified for working with triangles on a sphere.

More information about the Law of Cosines can be found in the Ask Dr. Math archives. A derivation of the Law of Cosines is one possible page you can visit when you explore 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.

Building Bridges - Leigh Nataro
Trig/Calc, difficulty level 3. Given some dimensions, find the length of a cable that lies along the diagonal of a bridge. ... more>>

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

Fishing on the Bay - Leigh Nataro
Trig/Calc, difficulty level 3. Will the depth of the water on the bay be at the right level for fishing? Write a trig function to find out. ... 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>>

Irregular Acreage - Leigh Nataro
Trig/Calc, difficulty level 2. Based on the given information, find the missing length of a lot in the shape of a quadrilateral. ... more>>

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

Managing a Mall - Leigh Nataro
Trig/Calc, difficulty level 2. Find how many square feet there are in a quadrilateral-shaped store. ... more>>

One Area - Many Solutions - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices. ... more>>

The Seal of Dalvek - Steve Earth
Trig/Calc, difficulty level 3. Discover the area of a circular segment based upon its circumference. ... 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>>

Swimming Sea Turtles - Leigh Nataro
Trig/Calc, difficulty level 4. Using latitude and longitude data collected from three sea turtles, determine how far each turtle is from its starting position. ... 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>>

Up, Up, and Away (Part I) - Leigh Nataro
Trig/Calc, difficulty level 4. Can you determine the shortest distance a balloon could travel from Essex Junction, Vermont, to Honolulu, Hawaii? ... more>>

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