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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. - PowerPoint PPT Presentation
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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?