Chapter 6 Trigonometry/Pre-Calculus Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____	1.	Given , , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.

A)		
B)		
C)		
D)		
E)		

____	2.	Given , , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.
A)		
B)		
C)		
D)		
E)		

____	3.	Solve the triangle, if it exists. Round answers to the nearest whole number.

A)		
B)		
C)		
D)		
E)	No triangle is formed.	

____	4.	Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer(s) to two decimal places.
A)		
B)		
C)		
D)		
E)	not possible	

____	5.	Find the missing length h in the given triangle. Round your final answer to the nearest tenth.

A)	17.3	
B)	6.7	
C)	8.1	
D)	20.9	
E)	16.8	

____	6.	The angles of elevation of the top of a tower with respect to points A and B are  and respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.

A)	90.5867 ft	
B)	69.5185 ft	
C)	93.1156 ft	
D)	73.9801 ft	
E)	87.5000 ft	

____	7.	Find the third side of the triangle. Round answer to two decimal places.

A)		
B)		
C)		
D)		
E)		

____	8.	Find the third side of the triangle. Round answer to the nearest whole number.

A)		
B)		
C)		
D)		
E)		

____	9.	Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

A)	17.44	
B)	14.01	
C)	16.58	
D)	10.58	
E)	15.72	

____	10.	Solve the triangle. Round answers to one decimal place.

A)		
B)		
C)		
D)		
E)		

____	11.	Sarah and Joy go for a hike. On the first leg, they walk 3.7 miles in the direction  On the second and final leg, they walk 2.7 miles in the direction  At the end of the hike, how far are they from their starting point? Round your final answer to the nearest ten thousandth.
A)	5.9857 mi	
B)	5.0807 mi	
C)	6.4000 mi	
D)	4.8370 mi	
E)	4.3367 mi	

____	12.	A square is inscribed in a circle of radius 24 inches. Find the area of the square.
A)	1162 in2	
B)	2304 in2	
C)	576 in2	
D)	1152 in2	
E)	2254 in2	

____	13.	Is it possible for a triangle to have sides , and ?
A)	yes	
B)	no	

____	14.	Which of the labeled points do the polar coordinates  correspond to?

A)	D	
B)	E	
C)	A	
D)	B	
E)	C	

____	15.	Find the polar coordinates  with  and   corresponding to the point with the following rectangular coordinates. 
A)		
B)		
C)		
D)		
E)		

____	16.	Find the polar coordinates  with  and   corresponding to the point with the following rectangular coordinates .
A)		
B)		
C)		
D)		
E)		

____	17.	Convert the rectangular equation  to polar form.
A)		
B)		
C)		
D)		
E)		

____	18.	Convert the rectangular equation  to polar form.
A)		
B)		
C)		
D)		
E)		

____	19.	Sketch the graph of the polar equation .
A)		
B)		
C)		
D)		
E)		

____	20.	Sketch the graph of the polar equation .
A)		
B)		
C)		
D)		
E)		

____	21.	Sketch the graph of the polar equation .
A)		
B)		
C)		
D)		
E)		

____	22.	Sketch the graph of the polar equation .
A)		
B)		
C)		
D)		
E)		

____	23.	Given  and , determine .
A)		
B)		
C)		
D)		
E)		

____	24.	Let u and v.  Find uv.
A)		
B)		
C)		
D)		
E)		

____	25.	Given  and , determine .
A)		
B)		
C)		
D)		
E)		

____	26.	Find the magnitude and direction for the vector. Round answers to one decimal place.

A)		
B)		
C)		
D)		
E)		

____	27.	Find a unit vector in the direction of .
A)		
B)		
C)		
D)		
E)		

____	28.	Find the component form of v if  and the angle it makes with the x-axis is .
A)		
B)		
C)		
D)		
E)		

____	29.	Find the dot product of the vectors  and 
A)	1	
B)	25	
C)		
D)		
E)	0	

____	30.	Given  and , find .
A)		
B)		
C)	13	
D)	31	
E)		

____	31.	Calculate where  and .
A)		
B)		
C)		
D)		
E)		

____	32.	Let  and . Decompose v into two vectors  and , where  is parallel to w and  is orthogonal to w.
A)		
B)		
C)		
D)		
E)