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Homework, Page 484

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Solve the triangle.

1.

Solve the triangle.

5.

Solve the triangle.

9.

State whether the given measurements determine zero, one, or two triangles.

13.

State whether the given measurements determine zero, one, or two triangles.

17.

Two triangles can be formed using the given measurements. Find both triangles.

21.

Decide whether the triangle can be solved using the Law of Sines. If so, solve it, if not, explain why not.

25.

Neither triangle can be solved using the Law of Sines, for the one on the left we need to know the length of the side opposite the known angle and for the one on the right, we have the same problem.

Respond in one of the following ways:

(a) State: “Cannot be solved with Law of Sines.”

(b) State: “No triangle is formed.”

(c) solve the triangle.

29.

No triangle is formed. The largest side of a triangle is opposite the largest angle and angle A must be the largest angle and side a is no the largest side.

Respond in one of the following ways:

(a) State: “Cannot be solved with Law of Sines.”

(b) State: “No triangle is formed.”

(c) solve the triangle.

33.

37. Two markers A and B on the same side of a canyon rim are 56 ft apart. A third marker C, located on the opposite rim, is positioned so that

(a) Find the distance between C and A.

(b) Find the distance between the canyon rims.

41. A 4-ft airfoil attached to the cab of a truck makes an 18º angle with the roof and angle β is 10º. Find the length of the vertical brace positioned as shown.

45. Two lighthouses A and B are known to be exactly 20 mi apart. A ship’s captain at S measures the angle S at 33º. A radio operator measures the angle B at 52º. Find the distance from the ship to each lighthouse.

49. The length x in the triangle is

(A) 8.6

(B) 15.0

(C) 18.1

(D) 19.2

(E) 22.6

53. (a) Show that there are infinitely many triangles with AAA given if the sum of the three positive angles is 180º.

Consider the triangle formed with its base on a radius that is one-half the diameter of a semi-circle. If the opposite ends of the radius are connected to a point on the semi-circle, a triangle is formed. Since there are an infinite number of possible values of the radius, there must be an infinite number of possible triangles.

53. (b) Give three examples of triangles where A = 30º, B = 60º, and C = 90º.

(c) Give three examples where A = B = C = 60º.

57. Towers A and B are known to be 4.1 mi apart on level ground. A pilot measures the angles of depression to the towers at 36.5º and 25º, respectively. Find distances AC and BC and the height of the aircraft.

5.6

The Law of Cosines

- Deriving the Law of Cosines
- Solving Triangles (SAS, SSS)
- Triangle Area and Heron’s Formula
- Applications
… and why

The Law of Cosines is an important extension of the

Pythagorean theorem, with many applications.

Find the area of a triangle with sides 10, 12, 14.

Find the area of a regular nonagon (9-sided) circumscribed about a circle of radius 10 in.

Tony must find the distance from point A to point B on opposite sides of a lake. He finds point C which is 860 ft from point A and 175 ft from point B. If he measures the angle at point C between points A and B as 78º, what is the distance between points A and B.

- Homework Assignment #1
- Review Section 5.6
- Page 494, Exercises: 1 – 53 (EOO)

- Two-Dimensional Vectors
- Vector Operations
- Unit Vectors
- Direction Angles
- Applications of Vectors
… and why

These topics are important in many real-world applications, such

as calculating the effect of the wind on an airplane’s path.

The velocity of a moving object is a vector

because velocity has both magnitude and

direction. The magnitude of velocity is speed.