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Lectures
2 Videos

An Introductory example of Solving Three Dimensional Problem by using Trigonometry

Find the height of the cliff.

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2.33mins

An Introductory example of Solving Three Dimensional Problem by using Trigonometry

Example of a Three Dimension 3D Problem

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4.17mins

Example of a Three Dimension 3D Problem

Solutions
17 Videos

Mina is trolling for salmon in Lake Ontario. She sets the fishing rod so that its tip is 1 m above water and the line forms an angle of `35^o`

with the water’s surface. She knows that there are fish at a depth of 45 m. Describe the steps you would use to calculate the length of line she must let out.

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1.47mins

Q1

Josh is building a garden shed that is 4.0 m wide. The two sides of the roof are equal in length and must meet at an angle of `80^o`

. There will be a 0.5 m overhang on each side of the shed. Josh wants to determine the length of each side of the roof.

**a)** Should he use the sine law or the cosine law? Explain.

**b)** How could Josh use the primary trigonometric ratios to calculate x?

Explain.

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1.42mins

Q2

Determine the value of `x`

to the nearest centimetre. Explain your reasoning for each step of your solution.

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1.12mins

Q3a

Determine the value of `x`

to the nearest centimetre and `\theta`

to the nearest degree. Explain your reasoning for each step of your solution.

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2.06mins

Q3b

`x`

to the nearest centimetre and `\theta`

to the nearest degree. Explain your reasoning for each step of your solution.

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3.04mins

Q3c

`x`

to the nearest centimetre and `\theta`

to the nearest degree. Explain your reasoning for each step of your solution.

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3.02mins

Q3d

As a project, a group of students was asked to determine the altitude, `h`

, of a promotional blimp. The students’ measurements are shown in the sketch at the left.

**a)** Determine h to the nearest tenth of a metre. Explain each of your steps.

**b)** Is there another way to solve this problem? Explain.

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2.07mins

Q4

While Trey and Bill were flying a hot-air balloon from Beamsville to Vineland in southwestern Ontario, they decided to calculate the straight-line distance, to the nearest metre, between the two towns.

- From an altitude of 226 m, they simultaneously measured the angle of depression to Beamsville as
`2^{\circ}`

and to Vineland as`3^{\circ}`

. - They measured the angle between the lines of sight to the two towns as
`80^{\circ}`

.

Is there enough information to calculate the distance between the two towns? Justify your reasoning with calculations.

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4.32mins

Q5

The observation deck of the Skylon Tower in Niagara Falls, Ontario, is 166 m above the Niagara River. A tourist in the observation deck notices two boats on the water. From the tourist's position,

- the bearing of boat
`A`

is`180^{\circ}`

at an angle of depression of`40^{\circ}`

. - the bearing of boat
`B`

is`250^{\circ}`

at an angle of depression of`34^{\circ}`

.

Calculate the distance between the two boats to the nearest metre.

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4.47mins

Q6

Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of `20^o`

. Paris, Juliet’s other suitor, is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of `18^o`

. Romeo and Paris are 100 m apart as shown. Determine the height ofJuliet’s balcony above the ground, to the nearest metre.

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3.41mins

Q7

A coast guard helicopter hovers between an island and a damaged sailboat.

- From the island, the angle of elevation to the helicopter is
`73^o`

. - From the helicopter, the island and the sailboat are
`40^o`

apart. - A police rescue boat heading toward the sailboat is 800 m away from the
scene of the accident. From this position, the angle between the island and the sailboat is
`35^o`

. - At the same moment, an observer on the island notices that the sailboat and police rescue boat are
`68^o`

apart.

Explain how you would calculate the straight-line distance, to the nearest metre, from the helicopter to the sailboat. Justify your reasoning with calculations.

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2.47mins

Q8

Briana and Tanya are standing 8.8 m apart on a dock when they observe a sailboat moving parallel to the dock. When the boat is equidistant between both girls, the angle of elevation to the top of its 8.0 m mast is `51^{\circ}`

for both observers. Describe how you would calculate the angle, to the nearest degree, between Tanya and the boat as viewed from Briana's position. Justify your reasoning with calculations.

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3.25mins

Q9

Bert wants to calculate the height of a tree on the opposite bank of a river. To do this, he lays out a baseline 80 m long and measures the angles as shown at the left. The angle of elevation from A to the top of the tree is `28^o`

. Explain if this information helps Bert to calculate the height of the tree to the nearest metre. Justify your reasoning with calculations.

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1.42mins

Q11

Channy's homework question reads like this:
Bill and Chris live at different intersections on the same street, which runs north to south. When both of them stand at their front doors, they see a hot-air balloon toward the east at angles of elevation of `41^o`

and `55^o`

, respectively. Calculate the distance between the two friends.

**a)** Channy says she doesn’t have enough information to answer the question. Evaluate Channy's statement. Justify your reasoning with calculations.

**b)** What additional information, if any, would you need to solve the problem? Justify your answer.

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1.44mins

Q12

Two roads intersect at `34^o`

. Two cars leave the intersection on different roads at speeds of 80 km/h and 100 km/h. After `2`

h, a traffic helicopter that is above and between the two cars takes readings on them. The angle of depression to the slower car is `20^o`

, and the straight—line distance from the helicopter to that car is `100`

km. Assume that both cars are travelling at constant speed.

- Calculate the straight—line distance, to the nearest kilometre, from the helicopter to the faster car. Explain your reasoning for each step of your solution.

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2.20mins

Q13a

Two roads intersect at `34^o`

. Two cars leave the intersection on different roads at speeds of 80 km/h and 100 km/h. After 2 h, a traffic helicopter that is above and between the two cars takes readings on them. The angle of depression to the slower car is `20^o`

, and the straight—line distance from the helicopter to that car is 100 km. Assume that both cars are travelling at constant speed.

- Determine the altitude of the helicopter to the nearest kilometre.

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0.30mins

Q13b