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Trigonometry
Triangles

1
The Law of Sines

Problem  1

In triangle \(ABC\), \(A=30^\circ\), \(B=70^\circ\), and \(a=8.0\) cm. Find the length of side \(c\).

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  2

Find the missing parts of triangle \(ABC\) if \(B=34^\circ\), \(C=82^\circ\), and \(a=5.6\) cm.

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  3
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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Adam cc
Adam
Julieta espanol spanish
Julieta
Problem  4

A hot-air balloon is flying over a dry lake when the wind stops blowing. The balloon comes to a stop \(450\) feet above the ground at point \(D\) as shown in Figure 9. A jeep following the balloon runs out of gas at point \(A\). The nearest service station is due north of the jeep at point \(B\). The bearing of the balloon from the service station at \(B\) is S \(19^\circ\) E. If the angle of elevation of the balloon from \(A\) is \(12^\circ\), how far will the people in the jeep have to walk to reach the service station at point \(B\)?

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Adam cc
Adam
Cynthia cc espanol spanish
Cynthia
Mini Lecture

Mini Lecture

  1. In \(\Delta ABC\), \(A=50^\circ\), \(B=60^\circ\), and \(a=36\) km. Find \(C\) and then find \(c\).

  2. In \(\Delta ABC\), \(B=13.4^\circ\), \(C=24.8^\circ\), and \(a=315\) cm. Find all the missing parts.

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Mr. McKeague cc
Mr. McKeague

2
The Ambiguous Case

Problem  1

Find angle \(B\) in triangle \(ABC\) if \(a=2\), \(b=6\), and \(A=30^\circ\).

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  2

Find the missing parts in triangle \(ABC\) if \(a=54\) cm, \(b=62\) cm, and \(A=40^\circ\).

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  3

Find the missing parts of triangle \(ABC\) if \(C=35.4^\circ\), \(a=205\) ft, and \(c=314\) ft.

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Stefanie cc
Stefanie
Cynthia cc espanol spanish
Cynthia
Mini Lecture

Mini Lecture
Solve \(\Delta ABC\) if

  1. \(A=30^\circ\), \(b=40\) ft, and \(a=10\) ft.

  2. \(A=120^\circ\), \(b=20\) cm, and \(a=30\) cm.

  3. \(A=38^\circ\), \(b=41\) ft, and \(a=54\) ft.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

3
The Law of Cosines

Problem  1

Find the missing parts of triangle \(ABC\) if \(A=60^\circ\), \(b=20\) inches, and \(c=30\) inches.

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  2

The diagonals of a parallelogram are \(24.2\) cm and \(35.4\) cm, and intersect at an angle of \(65.5^\circ\). Find the length of the shorter side of the parallelogram.

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  3

Solve triangle \(ABC\) if \(a=34\) km, \(b=20\) km, and \(c=18\) km.

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia cc espanol spanish
Cynthia
Problem  4

A plane is flying with an airspeed of \(185\) miles per hour with heading \(120^\circ\). The wind currents are running at a constant \(32\) miles per hour at \(165^\circ\) clockwise from due north. Find the true course and ground speed of the plane.

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Mr. Perez
Mr. Perez
Adam cc
Adam
Mini Lecture

Mini Lecture

  1. Solve \(\Delta ABC\) if \(a=410\) meters, \(c=340\) meters, and \(B=151.5^\circ\)

  2. If \(a=38\) meters, \(b=10\) meters, and \(c=31\) meters, find the largest angle.

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Mr. McKeague cc
Mr. McKeague

4
The Area of a Triangle

Problem  1

Find the area of the triangle \(ABC\) if \(A=35.1^\circ\), \(b=2.43\) cm, and \(c=3.57\).

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Julieta espanol spanish
Julieta
Problem  2

Find the area of triangle \(ABC\) given \(A=24^\circ 10'\), \(B=120^\circ 40'\), and \(a=4.25\) ft.

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Problem  3

Find the area of triangle \(ABC\) if \(a=12\) m, \(b=14\) m, and \(c=8.0\) m.

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Julieta espanol spanish
Julieta
Mini Lecture

Mini Lecture
Find the area of \(\Delta ABC\) if

  1. \(a=41.5\) meters, \(c=34.5\) meters, and \(B=151.5^\circ\).

  2. \(A=46^\circ\), \(B=95^\circ\), and \(c=6.8\) meters.

  3. \(a=4.8\) yards, \(b=6.3\) yards, and \(c=7.5\) yards.

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Mr. McKeague cc
Mr. McKeague