The four cases in which we can solve a triangle are ASA SSA SAS SSS. Which of the cases listed can lead to more than one solution (the ambiguous case)?

In which of the following cases must the Law of Cosines be used to solve a triangle? ASA SSS SAS SSA

Which of the following three triangle parts do not necessarily determine the other three parts? (A) AAS, (B) ASA, (C) SAS, (D) SSA, (E) SSS.

For triangle ABC with sides a, b, and c the Law of Cosines states

$$c ^ { 2 }$$

= ____

Sketch a triangle that has acute angle

$$\theta$$

, and find the other five trigonometric ratios of

$$\theta$$

.

$$\tan \theta = \sqrt { 3 }$$

Why is SSA called the ambiguous case?

The measures of two angles in standard position are given. Determine whether the angles are coterminal. 50°, 340°

The measures of two angles in standard position are given. Determine whether the angles are coterminal.

$$\frac { 5 \pi } { 6 } , \frac { 17 \pi } { 6 }$$

Solve triangle ABC. a = 20, b = 25, c = 22

Determine the singular values of the following matrices.

$$a. A=\left[\begin{array}{ll}{2} & {1} \\ {1} & {0}\end{array}\right]$$

$$b. A=\left[\begin{array}{ll}{2} & {1} \\ {1} & {0} \\ {0} & {1}\end{array}\right]$$

$$c. A=\left[\begin{array}{rr}{2} & {1} \\ {-1} & {1} \\ {1} & {1} \\ {2} & {-1}\end{array}\right]$$

$$d. A=\left[\begin{array}{rrr}{1} & {1} & {0} \\ {-1} & {0} & {1} \\ {0} & {1} & {-1} \\ {1} & {1} & {-1}\end{array}\right]$$

If P(x, y) is on the unit circle, then

$$x ^ { 2 } + y ^ { 2 }$$

= ____. So for all t we have

$$\sin ^ { 2 } t + \cos ^ { 2 }t$$

= ____.

Let P(x, y) be the terminal point on the unit circle determined by t. Then sin t = ____, cos t = ____, and tan t = ____.

The inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges. (a) The function

$$\sin ^ { - 1 }$$

has domain ____ and range ____. (b) The function

$$\cos^ { - 1 }$$

has domain ____ and range ____. (c) The function

$$\tan^ { - 1 }$$

has domain ____ and range _____.

A short-wave radio antenna is supported by two guy wires, 165 ft and 180 ft long. Each wire is attached to the top of the antenna and anchored to the ground at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of $67 ^ { \circ }$ with the ground. How far apart are the anchor points?