FOM 10: Chapter 3 Review: Trigonometry

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

____	1.	Determine the length of x, to the nearest tenth of a metre.

a.	5.2 m	c.	12.3 m	
b.	9.3 m	d.	14.7 m	

____	2.	Determine the length of x, to the nearest tenth of a centimetre.

a.	13.5 cm	c.	68.6 m	
b.	29.0 m	d.	75.7 m	

____	3.	Determine the length of x, to the nearest tenth of a centimetre.

a.	13.5 cm	c.	68.6 m	
b.	29.0 m	d.	75.7 m	

____	4.	Determine the length of x, to the nearest tenth of a metre.

a.	5.1 m	c.	23.6 m	
b.	11.7 m	d.	24.1 m	

____	5.	What is the value of tan 65° to 3 decimal places?
a.	0.423	c.	0.906	
b.	0.700	d.	2.145 	

____	6.	Determine the value of sin 38°, to 3 decimal places.
a.	0.380	c.	0.781	
b.	0.616	d.	0.788	

____	7.	Calculate the value of cos 38° to 3 decimal places.
a.	0.380	c.	0.781	
b.	0.616	d.	0.788	

____	8.	Determine the measure of A if tan A = 0.7813, to the nearest tenth of a degree.
a.	38.0°	c.	51.4°	
b.	38.6°	d.	62.0°	

____	9.	Determine the measure of A if sin A = 0.7813.
a.	38.0°	c.	51.4°	
b.	38.6°	d.	62.0°	

____	10.	Determine the measure of A if cos A = 0.7813.
a.	38.0°	c.	51.4°	
b.	38.6°	d.	62.0°	

Short Answer

	1.	What is the acronym for remembering trigonometric functions? 

	2.	To measure the width of a river, Kirstyn uses a large rock, an oak tree, and elm tree as reference points. Determine the width of the river, to the nearest tenth of a metre.

	3.	A field is 65 m long by 45 m wide. Petra walks diagonally across the field. What angle, with respect to the width of the field, does Petra’s path make? Answer to the nearest degree.

	4.	The side adjacent to the 74° angle in a right triangle is 6 cm long. How long is the hypotenuse, to the nearest tenth of a centimetre?

	5.	The side opposite from the 50° angle in a right triangle is 6 cm long. Determine the length of the hypotenuse.

	6.	Solve . Express each measurement to the nearest whole unit.

	7.	Solve . Express each measurement to the nearest whole unit.

8.  During take-off, a plane must rise at least 20 m during the first 1.5 km of flight to successfully clear the runway. What is the minimum angle the plane must make with the ground for a safe take-off, to the nearest hundredth of a degree?

Problem

	1.	A telephone pole is secured at its top with a guy wire, as shown. The guy wire makes an angle of 70° with the ground and is secured 5.6 m from the bottom of the pole. Determine the length of the guy wire, to the nearest tenth of a metre.

	2.	Susan and Jeremy are facing each other on opposite sides of a 10-m tall flagpole. The angle of elevation from Jeremy to the top of the flagpole is 50°. The angle of elevation from Susan to the top of the flagpole is 35°. To the nearest tenth of a metre, how far apart are Jeremy and Susan?

	3.	Alexa is looking up at her house from the backyard. From her point of view, the top of the house has an angle of elevation of 40°. The house is 15 m high. To the nearest metre, how far is Alexa from her house?

Use the information below to help answer the following questions.
At the bottom of a ski lift, there are two vertical poles: one 15 m tall and the other 8 m tall. The ground between the poles is level. The bases of the poles are 6 m apart. The poles are connected by two straight wires.

	4.	What angle does each wire make with the ground? Express your answer to the nearest degree.

	5.	What angle does each wire make with the top of its pole? Express your answer to the nearest degree.

Answer Section
MULTIPLE CHOICE
	1.	ANS:	A	PTS:	1	DIF:	B	OBJ:	Unit 1 Review
	2.	ANS:	B	PTS:	1	DIF:	B	OBJ:	Unit 1 Review

	3.	ANS:	A	PTS:	1	DIF:	B	OBJ:	Unit 1 Review

	4.	ANS:	C	PTS:	1	DIF:	B	OBJ:	Unit 1 Review

	5.	ANS:	D	PTS:	1	DIF:	A	OBJ:	Unit 1 Review

	6.	ANS:	B	PTS:	1	DIF:	A	OBJ:	Unit 1 Review
	7.	ANS:	D	PTS:	1	DIF:	A	OBJ:	Unit 1 Review

	8.	ANS:	A	PTS:	1	DIF:	A	OBJ:	Unit 1 Review

	9.	ANS:	C	PTS:	1	DIF:	A	OBJ:	Unit 1 Review

	10.	ANS:	B	PTS:	1	DIF:	A	OBJ:	Unit 1 Review

SHORT ANSWER

	1.	SohCahToa

	2.	ANS:	
The distance across the river is the distance between the rock and the oak tree (RO). 
The distance between the elm and oak trees (EO) is 12 m. The tangent of ÐREO is

The width of the river is approximately 36.9 m.

	3.	ANS:	

The angle is approximately 55°.

	4.	ANS:	

The hypotenuse is approximately 21.8 cm.

	5.	ANS:	

The hypotenuse is approximately 7.8 cm.

	6.	ANS:	

Angle C is 60°.
Use the cosine ratio to determine the length of side AC.

Side AC is 23 units.
Use the tangent ratio to determine the length of BC.

Side BC is 12 units.

	7.	ANS:	
Label the sides according to their corresponding angles

Angle C is 50°.

Side AC is approximately 29 units.
Use the cosine ratio to determine the length of BC.

Side BC is approximately 46 units.

	8.	ANS:	

The minimum angle the plane must make with the ground is 0.76°.

        
            PROBLEM

	1.	ANS:	

The guy wire is approximately 16.4 m long.
	Zx

	2.	ANS:	

Distance between Jeremy and Susan = 8.391 + 14.281
                                                       = 22.672...
Jeremy and Susan are approximately 22.7 m apart.

	3.	ANS:	

Alexa is approximately 18 m from her house.

	4.	ANS:	
For the longer wire:

For the shorter wire:

The longer wire makes an angle of approximately 68° with the ground. The shorter wire makes an angle of approximately 53° with the ground.

	5.	ANS:	
For the longer wire:

For the shorter wire:

The longer wire makes an angle of approximately 22° with the pole. The shorter write makes an angle of approximately 37° with the pole.