Need help with law of sines and cosines word problems!!

Question

Tom, Dick and Harry are camping in their tents. If the distance between Tom and Dick is 153 feet, the distance between Tom and Harry is 201 feet and the distance between Dick and Harry is 175 feet. What is the angle between Dick, Harry and Tom?

Answer 1

Note that this is an acute triangle (you don't even need to compute to see this; just note that 120-160-200 is a right triangle).

As we have three lengths and are trying to figure out an angle, this is a code that we use the cosine law.

Usually written a^2 = b^2 + c^2 - 2bc cos A, we may rewrite it as

A = arccos((b^2+c^2-a^2)/2bc); we multiply be 180/pi to convert to degrees. Note that we are looking for the angle opposite 153. Let a = 153, b = 175, and c = 201.

* 180/pi = 47.40 degrees

The other two angles are 57.35 and 75.25 degrees.

Answer 2

This is a straight application of the law of cosines.

Draw a picture!

153² = 201² + 175² - 2*175*201 * cos ∠DHT