Area of a Triangle

• Right Triangle:– Area = ½ base * height

• A triangle with a given angle:– Area = ½ a*b*sinC

• Area of a triangle with no given angles– Use Heron’s Formula– Area = √(s(s-a)(s-b)(s-c)), where s = (a + b + c)/2

Law of Cosines Applications – cont’d

• A florida highway must be built so that a bridge runs over any lake in its path

• A surveyor walks 250 yards from one end of a particular lake to a point next to the lake. He then turns at an angle of 70 degrees and walks 220 yards to the other end of the lake.

• How long is the horizontal distance of the lake?

Law of Cosine Applications

• 100 foot water tower to be built on a parcel of land that is not EXACTLY level.

• The left side of the hill makes a 6 degree angle depressed from the horizontal.

• Two “guy” wires are to be attached to the water tower, 75 feet uphill and 75 feet downhill from the base of the tower.

• Find the lengths of the guy wires.

Law of Sines Applications

• Vizzini’s boat is sailing toward The Cliffs of Insanity. He estimates the angle of elevation to be 15 degrees. A little while later, the boat has sailed 1200 feet closer to the cliffs, and he estimates the angle of elevation to be 50 degrees. – How tall are the Cliffs of Insanity?– How far is Vizzini’s boat from the Cliffs of Insanity

at the time of the second angle of elevation?

Arc Length Applications

• NYC is at 40.7 degrees latitude• Miami is at 25.7 degreesl atitude• The radius of the Earth is 3959 miles. • How far apart are NYC and Miami?