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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' quadrilateralshaped 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 quadrilateralshaped 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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