In general, sports involve tons and tons of Math.  Some sports and games, however, can use trigonometry for advantage.  Consider a golfer; for a right-handed golfer, a 

 is a shot that curves to the right of its intended path and a 

Suppose Se Ri Pak, playing in the US Women’s Open, hits the ball from the seventh tee - the shot is a 160-yard slice 4° from the path straight to the cup.  If the tee is 177 yards from the cup, how far does the ball now lie from the cup?  This situation exemplifies a great opportunity to use a new technique to ascertain this distance.

How is the Law of Cosines defined?  A proof-ish explanation

Given: ΔABC is a scalene triangle with no right angle.  This triangle is special, in that the sum of any two sides is greater than the length of the third side.  Without knowing any of the angles yet, we can set up the formula for finding any length of side based on the others with the following relationships.

Using the above image, you can see the angles labeled with capital letters and their corresponding, opposite sides with lowercase letters.  An altitude, or height (

 to the opposite ∠A at point D.  Now, segment AD divides side 

, derived from naming the pieces relative to the whole side 

.   Now, use the Pythagorean Theorem and the definition of the cosine ratio to show how ∠C, 

So, you can apply this method of defining relationships with the other sides by drawing similar heights from the other angles which give you the three formulas that are collectively known as the 

Once you include one of the angle measures, you can plug in values to the corresponding formula based on the relative triangle.  Looking back at the 

example, determine which properties of a triangle you are given that are relevant.   🔑

 a diagram for this situation using that given information.  What sides do you have?  Which part of the triangle are you looking for? 🔑Solve the problem involving the shot, ball location, and cup distance, rounding to the nearest tenth of a yard.

🔑Use the Law of Cosines along with the Law of Sines with the following two described triangles.  Draw a diagram and solve each triangle.  You may use a calculator and also round to the nearest tenth.

c) Using the solutions to a) and b), find the area of the two given triangles.  Use the formula for 

“Circa” is a term used throughout antiquity in order to 

when a person or civilization was born or perished.  Our friend, Hero (

), is no different - he was born circa (c.) 10 A.D. and never stopped experimenting until c. 70.  Hero of Alexandria was the first credited with harnessing the power of wind for machinery and developed a steam-powered engine.  He is also famous for his very own formula,

!  This formula describes the area of a triangle based solely on the side lengths.  The formula is as follows, where 

 = √[s(s - a)(s - b)(s - c)]  where s = ½(a + b + c)

Solve the following prompts completely.  Diagrams are recommended.  Use a calculator with inverse capability and round each answer to the nearest tenth units.

Students will utilize the Law of Cosines to solve trigonometric prompts and situations.

The Buddy Movie - Law of Cosines