Unit 4 notes - St John Brebeuf

Apprenticeship and workplace Math 11 

St.John Brebeuf 

Goals: 

Unit 4: 

Trigonometry of Right 

Triangles 

Mathematics 

Department 

In this chapter you will 

Use Trigonometry to calculate distances and angles. 

Solve complex problems by breaking them down into 2 or 3 right 

triangles. 

Use right triangles to solve problems in 3-D 

Key Terms: You will be able to define and use the following terms: 

2 angled problem 

3 angled problem 

4.1 Solving for Angles, Lengths and Distances: 

‣ Transit: a surveying instrument used to measure horizontal and 

vertical angles. 

Opposite 

Hypotenuse 

 

Adjacent 

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Sin = Cos = Tan = 

Example 1: 

Ethan buys a used portable conveyor for stockpiling landscaping 

materials such as gravel in his maintenance yard. The conveyor has a 

length along the belt of 12m, and makes a maximum angle of 15 with 

the ground. 

a) Sketch the conveyor. Label your diagram with your information. 

b) What is the maximum height of gravel stockpile this conveyor can 

make 

c) The gravel stockpile is in the shape of a cone and makes an angle of 

37 with the ground. What volume of material can Ethan store in the 

stockpile 

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Solution: 

a) 15 

12m 

h 

15 

b) SOH-CAH-TOA 

c) 

3.106m 

37 

r 

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Calculate r the radius of the cone: 

SOH-CAH-TOA 

Calculate the volume of the cone 

Volume cone 

= x area of base x height 

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B 

O D A 

Chord = BC 

Radius =OB=OA=OC 

C 

‣ Chord: a line that links two points on the circumference of the 

circle. 

Example 2: 

A rancher who lives near 100 Mile House, BC, has a piece of property 

shown on the plan below. He is planning to build a new fence, using 3 

strands of barbed wire around the perimeter. How much wire will he 

need for the fence 

200m 

a 

100 

b 

500m 

50 

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Solution: 

Split the property into 2 right triangles and a rectangle 

a 

200m 

e 

100 f c b 

d 

500m 

50 

Solve the right triangles to find c,d,e and f 

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Find a = c – f and b = d + e 

Calculate the perimeter 

*** 3 strands of barbed wire!!!!!! 

Example 3: 

Li is making a kite for a festival, as shown in the diagram 

45cm 

e 

45 a 30 

d 

b 

g c f 

a) What will be the length of the 

2 cross pieces that will be the 

frame 

b) Calculate the length of the 

string that will form the outer 

perimeter of the kite. 

c) What area of fabric will be 

needed to cover the whole kite 

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Solution: 

a) The length of the 2 cross pieces are a + c and b + d 

We need to solve each of the right triangles so number them 1-4 

so we can refer to each one and keep track of our calculations. 

1. 

2. 

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3. 

4. 

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b) Perimeter of the kite = 45 + e + f + g 

c) 

Area 1 = Area 2 = 

Area 3 = Area 4 = 

Complete notebook assignment page 177 # 1-10 odd 

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4.2: Solving Complex Problems in the Real World: 

Example1: 

A tunnel through a hill has an angle of elevation of 3.5, and a direction 

of 22 north of east. The length of the tunnel along its floor is 1400m. 

Examine the diagram below: 

3.5 1400m Exit B 

Entrance A h Elevation C 

22 

North 

East 

a) What is the difference in elevation between the entrance and the 

exit of the tunnel 

b) How far north of the entrance is the tunnel exit 

c) How far east of the entrance is the tunnel exit 

Solution: 

a) To calculate the difference in elevation draw triangle ABC 

1400m 

B 

3.5 

A h C 

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b) To calculate how far north and east of the tunnel you need to 

calculate the distance between the entrance and exit ie h in the 

triangle above. 

1400m 

B 

3.5 85m 

A h C 

You can use SOH-CAH-TOA or Pythagorean Theorem to find h 

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Now find the distance north 

22 

1397 

east 

north 

c) Now find the distance east 

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Example 2: 

Justin is laying out a ramp to go up a 30 slope in a park. Because the 

ramp may not have a slope greater than 1:20 so it can be used 

comfortably by wheelchairs and motorized scooters, he must angle it 

across the slope. The total change in elevation is 4 feet. 

Insert picture page 187 

a) What is the angle that the ramp must make with the base of the 

hill 

b) What width of hill is needed to build the ramp without using a 

switchback 

c) How can Justin used the calculated information to lay out the ramp 

without having to measure an angle on the slope 

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Solution: 

a) To calculate angle A we need l and b 

We know that the ramp has a slope of 1:20 

Tan C = 

Find C 

Use C to find l 

4 l 

2.862 

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Now find b 

4 b 

30 

Use l and b to find A 

b 

l 

A 

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b) You can use SOH-CAH-TOA or Pythagorean Theorem to find w 

l 

b 5.731 

w 

c) 

_____________________________________________________ 

_____________________________________________________ 

_____________________________________________________ 

_____________________________________________________ 

‣ Angle of Elevation: The angle formed between the horizontal 

and the line of sight when looking upwards. Sometimes it is 

referred to as the angle of inclination 

Line of sight 

Angle of elevation 

Horizontal 

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‣ Angle of Depression: The angle formed between the horizontal 

and the line of sight when looking downwards. 

Horizontal 

Angle of depression 

Line of sight 

‣ Clinometer: An instrument for measuring angles of elevation and 

depression 

Example 3: 

Ellie is standing on the edge of a building. She can see that the angle 

of elevation to the top of the next building is 46 and the angle of 

depression to the bottom of the building is 62. If the building is 30m 

away, how tall is the building 

y 

x 

46 

622 62 

30m 

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Solution: 

To find the solution we need to calculate x + y 

First we need to find x and y 

30 

62 

Y 

x 

46 

30 

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Example 4: 

Captain Ji sights an island in the distance. He uses a clinometer to 

measure the angle of elevation to the top of the Island as 32. He 

sails 400m closer to the island and takes another sighting. The angle 

of elevation from this closer position is 58. 

What is the height of the island 

Solution: 

Draw a good diagram of the situation 

A 

y 

B 58 D 32 C 

X 

400m 

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1 st use the tan ratio for triangle ABD 

A 

y 

B 58 D 

X 

2 nd use the tangent ratio for triangle ABC 

A 

y 

B 32 C 

x + 400 

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3 rd solve the pair of equations 

Complete notebook assignment page 195 # 1-7 

Complete Unit Review page 202 # 1-12 even 

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Reflect on your learning 

Now check the box that applies to you : 

RED 

AMBER GREEN 

I understand all the key terms. 

I can solve problems with more 

than one right triangle, using 

SOH-CAH-TOA and 

Pythagorean Theorem. 

I can solve problems involving 

right triangles in 2 -D. 


right triangles in 3 -D. 

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Angles of elevation and angle of 

depression. 

I have completed all 

homework assignments. 

I have attended tutorials 

for extra help. 

I am ready to sit my 

unit 4 test. 

Target: 

In my Unit Test I hope to achieve 

% 

Student’s Signature ____________________ 

Date__________ 

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Unit 4 notes - St John Brebeuf

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