Question 1

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.&#10;

Accepted Answer

To solve the triangle, first find angle A using the fact that the sum of angles in a triangle is 180 degrees: $A = 180^\circ - B - C = 180^\circ - 15.8^\circ - 102.9^\circ = 61.3^\circ$. Then, use the Law of Sines to find sides a and c: $\frac{a}{\sin A} = \frac{b}{\sin B}$ and $\frac{c}{\sin C} = \frac{b}{\sin B}$. Solving these equations gives $a \approx 108.6$ and $c \approx 120.6$, rounding to the nearest tenth.

Question 2

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;B, a, and c&#10;A) Yes&#10;B) No

Accepted Answer

B

Question 3

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

Using the Law of Sines, we can find the possible values for angle A and side a. Since $\sin(B)/b = \sin(A)/a$, we can solve for a. However, given the information, there's a possibility of having two different triangles due to the ambiguous case of the Law of Sines (when given two sides and a non-included angle). This occurs when the height (h) from the angle to the opposite side can be less than the given side (b), allowing for two different angles (and thus two different triangles) that satisfy the given conditions. Since $B = 46^\circ$, $b = 24$, and $c = 29$, and given that $29 > 24$, there's enough length in side c to potentially create two different triangles, one acute and one obtuse, depending on the specific measurements. This is why the correct answer is 2, indicating the possibility of two distinct triangles.

Question 4

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

The answer of Determine the number of triangles ABC possible...

Question 5

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

Given $a = 35$, $b = 46$, and $A = 21^\circ$, we use the Law of Sines to find the possible values for angle $B$. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B}$. Substituting the given values, we can solve for $\sin B$. However, because the sine function has two values for angles between $0^\circ$ and $180^\circ$ (one in the first quadrant and one in the second), there can be two different triangles formed, one with an acute angle $B$ and one with an obtuse angle $B$, as long as $\sin B$ yields a valid value less than or equal to 1. This results in two possible triangles, assuming angle $B$ does not violate the triangle sum theorem (the sum of angles in a triangle is $180^\circ$).

Question 6

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;b, C, and B&#10;A) Yes&#10;B) No

Accepted Answer

The law of sines can be used to solve for a missing side length or angle measure in a triangle when given either:
1. Two angle measures and any side length OR
2. Two side lengths and the angle opposite one of the side lengths
In this case, we are given the side length b and the measures of angles C and B. We can use the law of sines to solve for the remaining side and angle measures. Therefore, there is sufficient information for solving the triangle.

Question 7

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;a, A, and C&#10;A) Yes&#10;B) No

Accepted Answer

To solve a triangle using the law of sines, you need at least one side-length and its opposite angle. Here, you have a side (a) and its opposite angle (A), along with another angle (C), which is enough to find the third angle (B) using the angle sum property of triangles (A + B + C = 180°) and then apply the law of sines to find the remaining sides.

Question 8

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;a, c, and C&#10;A) Yes&#10;B) No

Accepted Answer

The law of sines can be used to solve a triangle when two angles and a non-included side are known or two sides and a non-included angle are known. In this case, with side a, side c, and angle C given, there is sufficient information to solve the triangle using the law of sines, as angle C can help find the ratio of the sides a and c.

Question 9

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

The answer of Determine the number of triangles ABC possible...

Question 10

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;b, A, and B&#10;A) Yes&#10;B) No

Accepted Answer

The law of sines can be used to solve for any missing side or angle in a triangle if we are given the measure of an angle and its opposite side, as well as the measure of another angle. Therefore, knowing the measures of sides b and angles A and B is sufficient information for solving the triangle by the law of sines.

Question 11

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;a, b, and C&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether there is sufficient information for...

Question 12

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;A, c, and a&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether there is sufficient information for...

Question 13

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.&#10;

Accepted Answer

The answer of Solve the triangle. Round to the nearest...

Question 14

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;b, B, and c&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether there is sufficient information for...

Question 15

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

The answer of Determine the number of triangles ABC possible...

Question 16

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;C, c, and A&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether there is sufficient information for...

Question 17

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.&#10;

Accepted Answer

The answer of Solve the triangle. Round to the nearest...

Question 18

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.&#10;

Accepted Answer

The answer of Solve the triangle. Round to the nearest...

Question 19

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,&#10;by the law of sines.&#10;a, b, and c&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether there is sufficient information for...

Question 20

Determine the number of triangles ABC possible with the given parts.&#10;

Accepted Answer

The answer of Determine the number of triangles ABC possible...

Question 21

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 22

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 23

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 24

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 25

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 26

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 27

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 28

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 29

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 30

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 31

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 32

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 33

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 34

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 35

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 36

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 37

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 38

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 39

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 40

Find the missing parts of the triangle.&#10;

Accepted Answer

The answer of Find the missing parts of the triangle.&#10;...

Question 41

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 42

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.&#10;

Accepted Answer

The answer of Find the area of triangle ABC with...

Question 43

Find the indicated angle or side. Give an exact answer.&#10;Find the measure of angle A in degrees.

Accepted Answer

The answer of Find the indicated angle or side. Give...

Question 44

Find the indicated angle or side. Give an exact answer.&#10;Find the exact length of side a.

Accepted Answer

The answer of Find the indicated angle or side. Give...

Question 45

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.&#10;

Accepted Answer

The answer of Find the area of triangle ABC with...

Question 46

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 47

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.&#10;

Accepted Answer

The answer of Find the area of triangle ABC with...

Question 48

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide
whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, b, and B

A) ASA; law of cosines
B) SSA; law of sines
C) ASA; law of sines
D) SSA; law of cosines

Accepted Answer

The answer of Assume a triangle ABC has standard labeling....

Question 49

Find the indicated angle or side. Give an exact answer.&#10;

Accepted Answer

The answer of Find the indicated angle or side. Give...

Question 50

Solve the problem.&#10;A rocket tracking station has two telescopes A and B placed 2.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the&#10;Distance to the rocket from telescope B at the moment when both tracking stations are directly east&#10;Of the rocket telescope A reports an angle of elevation of 20&#176; and telescope B reports an angle of&#10;Elevation of 52&#176;? Round to the nearest hundredth of a mile.&#10;A) 0.91 mi&#10;B) 1.36 mi&#10;C) 4.84 mi&#10;D) 3.12 mi

Accepted Answer

The answer of Solve the problem.&#10;A rocket tracking station has...

Question 51

Find the indicated angle or side. Give an exact answer.&#10;Find the measure of angle A in degrees.

Accepted Answer

The answer of Find the indicated angle or side. Give...

Question 52

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 53

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 54

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 55

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 56

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide
whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, b, and B

A) ASA; law of cosines
B) SSA; law of sines
C) ASA; law of sines
D) SSA; law of cosines