Unit 5 Review
Show all work for full credit.

Short Answer

	1.	The top of a 70-foot ramp is placed 42 feet above the base of the building.  The bottom of the ramp is 56 feet from the building. 
 
Which ratio represents the sine of ÐT? 

Find the value of x. Round to the nearest tenth.

	2.	

	3.	

	4.	A piece of art is in the shape of an equilateral triangle with sides of 13 in. Find the area of the piece of art. Round your answer to the nearest tenth.

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	5.	Find the value of x and y rounded to the nearest tenth.

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

	6.	

	7.	

Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.

	8.	

	9.	Find the missing value to the nearest tenth.

Simplify the radical expression.

	10.	

	11.	

	12.	

	13.	Triangle ABC has sides a = 15 and b = 4.  The included angle C has a measure of 40°.  What is the area of the triangle?  

	14.	In triangle ABC,  is a right angle and  45°. Find BC. If you answer is not an integer, leave it in simplest radical form.

	15.	Use the Law of Sines. Find b to the nearest tenth.       

	16.	In right Triangle ABC,  is the hypotenuse,  =  and .  What is the length of ?

	17.	Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

Find the value of x. Round to the nearest degree.

	18.	

	19.	Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.

	20.	Right triangle ABC has sides of length 5, 12, and 13. Right triangle DEF  is similar to ABC , but each side is three times longer than the corresponding side of ABC .

What do you know about the sin of ÐD and the sin of ÐA?

	21.	Triangle  GHI  is similar to triangle  JKL . Altitudes are drawn from vertices  H  and  K .

Which equation correctly describes the relationship between angles  G  and  J ?
a. sin J= sin I          b. sin J = sin G          c. sin L = cos G          d. sin L= tan G
	22.	Write the ratios for sin A and cos A.

	23.	A gardener needs to cultivate a triangular plot of land. One angle of the garden is 77, and two sides adjacent to the angle are 32 feet and 52 feet. To the nearest tenth, what is the area of the plot of land? 

Find the value of x. Round your answer to the nearest tenth.

	24.	

	25.	

	26.	Write the tangent ratios for  and .

27.	Find the length of the hypotenuse.

	28.	Use the Law of Cosines. Find b to the nearest tenth.  

	29.	The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the line of sight (hypotenuse) to the top of the building.

	30.	

What is the value of the cos R?

Simplify the radical expression by rationalizing the denominator.

	31.	

Find the value of x to the nearest degree.

	32.	

Find the area of the regular polygon. Give the answer to the nearest tenth.

	33.	hexagon with side 8 yd  

	34.	pentagon with side 6 ft  

	35.	A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far from the ladder is the base of the slide?

	36.	A conveyor belt carries supplies from the first floor to the second floor, which is 16 feet higher. The belt makes a 60° angle with the ground.

	37.	In a right triangle PQR, sin P =  and cos P = .  What is the value of tan P?

	38.	The area of a square garden is 50 m2. How long is the diagonal?
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	39.	

What is the correct ratio for the tan B?

	40.	Use the Law of Sines. Find  to the nearest tenth.