Sections 10.1-10.2 Law of Cosines and Law of Sines Created by Educational Technology Network. www.edtechnetwork.com 2009 ONLINE STOP WATCH

REVIEW JEOPARDY RULES ONE PERSON WILL ANSWER THE QUESTION FOR EACH GROUP ANSWERS SHOULD BE TO THE TENTHS DECIMAL PLACE. GROUPS CANNOT WHISPER ANSWERS TO THIER PERSON OR HELP THEM IN ANY WAY EVERYONE MUST TAKE A TURN ANSWERING A QUESTION ONCE YOU RING IN, YOU HAVE 5 SECONDS TO ANSWER ANSWERS DO NOT HAVE TO BE IN QUESTION FORM EVERYONE SHOULD BE DOING EACH PROBLEM. YOUR WORK WILL BE CHECKED AT THE END OF THE PERIOD.

Area of an Oblique Triangle REVIEW JEOPARDY Law of Cosines Law of Sines Ambiguous Cases Area of an Oblique Triangle Heron’s Formula 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50

Find the missing parts of the oblique triangle with Law of Cosines– 10 Points Find the missing parts of the oblique triangle with B = 40º, a = 12, and c = 20. b ≈ 13.3, A ≈ 35.5º, and C ≈ 104.5º

Find the angles of a triangle whose vertices are Law of Cosines– 20 Points Find the angles of a triangle whose vertices are A(0,0), B(5,-2), and C(1,-4). A ≈ 54.2º, B ≈ 48.4º, and C ≈ 77.4º

Law of Cosines– 30 Points Two trains leave a station on different tracks. The tracks make a 112º angle with the station as a vertex. The first train travels at an average speed of 90 kilometers per hour and the second at an average speed of 55 kilometers per hour. How far apart are they after 2 hours and 45 minutes? 334.9 km

Law of Cosines– 40 Points The pitcher’s mound on a standard baseball diamond (which is actually a square) is 60.5 feet from home plate. How far is the pitcher’s mound from first base? 63.7 feet

Law of Cosines– 50 Points Two ships leave port, one traveling in a straight course at 22 mph and the other traveling in a straight course at 31 mph. The courses diverge at 38º. How far apart are they after 3 hours? 57.7 miles

Find the missing parts of the oblique triangle with Law of Sines– 10 Points Find the missing parts of the oblique triangle with B = 33º, C = 46º, and b = 4. A = 101º, a ≈ 7.2, and c ≈ 5.3

Find the missing parts of the oblique triangle with Law of Sines– 20 Points Find the missing parts of the oblique triangle with B = 97.5º, C = 42.5º, and b = 7 a ≈ 4.5, c ≈ 4.8, and A = 40

Find the missing parts of the oblique triangle with Law of Sines– 30 Points Find the missing parts of the oblique triangle with a = 9, b = 14, and B = 95º. A ≈ 39.8º, C ≈ 45.2º, and c ≈ 10.0

Law of Sines– 40 Points A side view of a bus shelter is shown in the following figure. The brace d makes an angle of 37.25º with the back and an angle of 34.85º with the top of the shelter. How long is the brace? 5.0 feet

Law of Sines– 50 Points Two straight roads meet at an angle of 40º in Harville, one leading to Eastview and the other to Wellston (see figure). Eastview is 18 kilometers from Harville and 20 kilometers from Wellston. What is the distance from Harville to Wellston? 30.1 km

Ambiguous Cases– 10 Points Find the missing parts of the oblique triangle with b = 30, c = 50, and C = 60º. A ≈ 88.7º, B ≈ 31.3º, and a ≈ 57.7

Ambiguous Cases– 20 Points Find the missing parts of the oblique triangle with b = 15, c = 25, and B = 47º. No solution

Ambiguous Cases– 30 Points Find the missing parts of the oblique triangle with a = 50, c = 80, and C = 45º. A ≈ 26.2º, B ≈ 108.8º, and b ≈ 107.1

Ambiguous Cases– 40 Points Find the missing parts of the oblique triangle with b = 24.1, c = 10.5, and C = 26.3º. No solution

Ambiguous Cases– 50 Points Find the missing parts of the oblique triangle with a = 30, b = 40, and A = 30º. 1: B ≈ 41.8º, C ≈ 108.2º, and c ≈ 57.0 2: B ≈ 138.2º, C ≈ 11.8º, and c ≈ 12.3

Area of an Oblique Triangle– 10 Points Find the area of a triangle with b = 10, c = 14, and A = 36º 41.1 sq units

Area of an Oblique Triangle– 20 Points Find the area of a triangle with a = 9, b = 13, and C = 75º 56.5 sq units

DAILY DOUBLE Area of an Oblique Triangle– 30 Points Find the area of a triangle with a = 17, b = 27, and c = 40 177.6 sq units

Area of an Oblique Triangle– 40 Points Find the area of a triangle with vertices A(0,0), B(2,-5), and C(-3,1). 6.5 sq units

Area of an Oblique Triangle– 50 Points Find the area of the triangle ABE. B A C 393.9 sq units E D

Heron’s Formula– 10 Points Find the area of a triangle with a = 4, b = 12, c = 14. 22.2 sq units

Heron’s Formula– 20 Points Find the area of a triangle with a = 7, b = 9, and c = 11. 31.4 sq units

Heron’s Formula– 30 Points Find the area of a triangle with c = 7, a = 10, B = 68º. 32.4 sq units

Heron’s Formula– 40 Points If a gallon of paint covers 400 square feet, how many one gallon buckets are needed to paint a triangular deck with the sides of 65 feet, 72 feet, and 88 feet? 6 buckets

Heron’s Formula– 50 Points What is the area of a triangle whose sides have lengths 12, 20, and 36? (HINT: Draw a picture of the triangle) The triangle does not exist.