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Area of a Triangle

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.

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Area of a Triangle

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  1. 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

  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?

  3. 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.

  4. 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?

  5. Arc Length Applications • NYC is at 40.7 degrees latitude • Miami is at 25.7 degreeslatitude • The radius of the Earth is 3959 miles. • How far apart are NYC and Miami?

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