Sections 10.1-10.2Law of Cosines

and Law of Sines

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REVIEW JEOPARDY RULES

REVIEW JEOPARDYHeron’s Formula

Area of an Oblique Triangle

Ambiguous CasesLaw of SinesLaw of

Cosines

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Law of Cosines– 10 PointsFind 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

Law of Cosines– 20 PointsFind 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 PointsTwo 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 PointsThe 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 PointsTwo 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

Law of Sines– 10 PointsFind the missing parts of the oblique triangle with B = 33º, C = 46º, and b

= 4.

A = 101º, a ≈ 7.2, and c ≈ 5.3

Law of Sines– 20 PointsFind the missing parts of the

oblique triangle with B = 97.5º, C = 42.5º, and b

= 7a ≈ 4.5, c ≈ 4.8, and A = 40

Law of Sines– 30 PointsFind 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 PointsA 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 PointsTwo 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 withb = 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 PointsFind 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 ≈ 57.02: 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 =

36º41.1 sq units

Area of an Oblique Triangle– 20 Points

Find the area of a triangle with a = 9, b = 13, and C =

75º56.5 sq units

Area of an Oblique Triangle– 30 Points

Find the area of a triangle with a = 17, b = 27, and c =

40177.6 sq units

DAILY DOUBLE

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 PointsFind the area of the

triangle ABE.

393.9 sq units

A B

E

C

D

Heron’s Formula– 10 PointsFind the area of a triangle with a = 4, b = 12, c = 14.

22.2 sq units

Heron’s Formula– 20 PointsFind the area of a triangle with a = 7, b = 9, and c =

11.

31.4 sq units

Heron’s Formula– 30 PointsFind the area of a triangle

with c = 7, a = 10, B = 68º.

32.4 sq units

Heron’s Formula– 40 PointsIf 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 PointsWhat 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.